would this work for a quadratic equation?

Yes because you will want you to check to see if you have the right solution.

A "system" of equations is a set or collection of equations that you deal with all together at once.

Does a single linear equation with two or more unknowns always have infinitely many solutions

Yes, that's right. You could choose whatever values you like for all but one of the variables, and then final variable can always be made to fit. For example, if you had the equation `ax + by + cz = k`, then whatever you pick for `y` and `z`, you can solve for `x` to get `x = (k - by - cz)/a`, and the equation will be satisfied.

is it just me or am i just really dumb? nothing makes sense

By now you should be familiar with the concept of testing solutions to equations by using substitution. If you are asked if a point is a solution to an equation, we replace the variables with the given values and see if the 2 sides of the equation are equal (so is a solution), or not equal (so not a solution). A solution to a system of equations means the point must work in both equations in the system. So, we test the point in *both* equations. It must be a solution for both to be a solution to the system. Hope this helps.

Would this work for quadratic equations?

Since you are testing the point for each equation independent of each other, it would work for any function. If you have two quadratic equations, there is also a possibility of having two different intersections, not just one.

I have perfectly parallel lines, so is there a solution? I can't figure out this problem.

Parallel lines will never cross so a system of parallel lines will have no solution. As a reminder, parallel lines have the exact same slope.

im stupid i dont get this

Bro chill. A solution of an equation is when both sides (i.e., LHS and RHS) become equal. What do you need to do to make both sides equal? Well, you need to find some values for X and Y so that they become equal when you plug X values wherever X and Y are. Here, some of the solutions are given, but we need to check after plugging them in it makes both sides of the equation equal. (like 1 = 1 , 2 = 2, BUT if you get 1 = 2, or 3 = 4 it is clear that it is false and hence the values of X or Y or both are wrong and hence, not the solution[s] )

can u make an example more easier

The example in the video is about as simple as it gets. Neither equation has fractions or decimals. The video is show you how to determine if an ordered pair (a point) is a solution to a system of equation. Sal has one point that he is testing to see if it is a solution to the system. In order for this to be true, the point must work in both equations (i.e., the 2 sides of each equation come out equal). He does the test by substituting the values from the ordered pair into each equation and simplifying. -- The point works in the 1st equation. -- The point did not work in the 2nd equation. This tells us the point in on the line created by the first equation, but it is not a point on the line created by the 2nd equation. Remember, to be solution to the system, the point must work for both equations. Since it didn't, the point is not a solution to the system. Hope this helps.

*What does a system mean here*?

A system of equations just means at least 2 equations. For a single solution in a system of equations, you need as many independent equations as you have variables.

Main content

8th grade (Eureka Math/EngageNY)

Course: 8th grade (Eureka Math/EngageNY) > Unit 4

Lesson 4: Topic D: Systems of linear equations and their solutions

Testing a solution to a system of equations

Name: Testing a solution to a system of equations
Uploaded: 2011-03-16T18:27:52Z
Description: Sal checks whether (-1,7) is a solution of the system: x+2y=13 and 3x-y=-11.

Google Classroom

Sal checks whether (-1,7) is a solution of the system: x+2y=13 and 3x-y=-11. Created by Sal Khan and Monterey Institute for Technology and Education.

Want to join the conversation?

Sort by:

yanicknorman
Posted 9 years ago. Direct link to yanicknorman's post “What is system?”
What is system?
Button navigates to signup pageComment on yanicknorman's post “What is system?”
(27 votes)
Answer
- Minnoc
  Posted 2 years ago. Direct link to Minnoc's post “A "system" of equations i...”
  A "system" of equations is a set or collection of equations that you deal with all together at once.
  Comment on Minnoc's post “A "system" of equations i...”
  (5 votes)
ashantiharrisalgebra
Posted 12 years ago. Direct link to ashantiharrisalgebra's post “would this work for a qua...”
would this work for a quadratic equation?
Button navigates to signup pageComment on ashantiharrisalgebra's post “would this work for a qua...”
(33 votes)
Answer
- Leigh, Daniel; 200409266
  Posted 6 years ago. Direct link to Leigh, Daniel; 200409266's post “Yes because you will wan...”
  Yes because you will want you to check to see if you have the right solution.
  Button navigates to signup page
  (4 votes)
Leslie Ganzwa
Posted 8 years ago. Direct link to Leslie Ganzwa's post “Does a single linear equa...”
Does a single linear equation with two or more unknowns always have infinitely many solutions
Button navigates to signup pageButton navigates to signup page
(12 votes)
Answer
- Alex
  Posted 8 years ago. Direct link to Alex's post “Yes, that's right. You co...”
  Yes, that's right. You could choose whatever values you like for all but one of the variables, and then final variable can always be made to fit.
  For example, if you had the equation ax + by + cz = k, then whatever you pick for y and z, you can solve for x to get x = (k - by - cz)/a, and the equation will be satisfied.
  Button navigates to signup page
  (21 votes)
Leigh, Daniel; 200409266
Posted 6 years ago. Direct link to Leigh, Daniel; 200409266's post “Would this work for quadr...”
Would this work for quadratic equations?
Button navigates to signup pageComment on Leigh, Daniel; 200409266's post “Would this work for quadr...”
(7 votes)
Answer
- David Severin
  Posted 6 years ago. Direct link to David Severin's post “Since you are testing the...”
  Since you are testing the point for each equation independent of each other, it would work for any function. If you have two quadratic equations, there is also a possibility of having two different intersections, not just one.
  Button navigates to signup page
  (14 votes)
Sara Velasco
Posted 7 years ago. Direct link to Sara Velasco's post “I have perfectly parallel...”
I have perfectly parallel lines, so is there a solution? I can't figure out this problem.
Button navigates to signup pageComment on Sara Velasco's post “I have perfectly parallel...”
(7 votes)
Answer
- KathyC
  Posted 7 years ago. Direct link to KathyC's post “Parallel lines will never...”
  Parallel lines will never cross so a system of parallel lines will have no solution.
  As a reminder, parallel lines have the exact same slope.
  Button navigates to signup page
  (14 votes)
jeremy jones
Posted 4 years ago. Direct link to jeremy jones's post “im stupid i dont get this”
im stupid i dont get this
Button navigates to signup pageButton navigates to signup page
(7 votes)
Answer
- HRSH.
  Posted 4 years ago. Direct link to HRSH.'s post “Bro chill. A solution of ...”
  Bro chill. A solution of an equation is when both sides (i.e., LHS and RHS) become equal. What do you need to do to make both sides equal? Well, you need to find some values for X and Y so that they become equal when you plug X values wherever X and Y are.
  
  Here, some of the solutions are given, but we need to check after plugging them in it makes both sides of the equation equal. (like 1 = 1 , 2 = 2, BUT if you get 1 = 2, or 3 = 4 it is clear that it is false and hence the values of X or Y or both are wrong and hence, not the solution[s] )
  Comment on HRSH.'s post “Bro chill. A solution of ...”
  (7 votes)
mwp07
Posted 3 years ago. Direct link to mwp07's post “is it just me or am i jus...”
is it just me or am i just really dumb? nothing makes sense
Button navigates to signup pageComment on mwp07's post “is it just me or am i jus...”
(8 votes)
Answer
- Kim Seidel
  Posted 3 years ago. Direct link to Kim Seidel's post “By now you should be fami...”
  By now you should be familiar with the concept of testing solutions to equations by using substitution. If you are asked if a point is a solution to an equation, we replace the variables with the given values and see if the 2 sides of the equation are equal (so is a solution), or not equal (so not a solution).
  
  A solution to a system of equations means the point must work in both equations in the system. So, we test the point in both equations. It must be a solution for both to be a solution to the system.
  
  Hope this helps.
  Comment on Kim Seidel's post “By now you should be fami...”
  (6 votes)
joseline.ramirez
Posted 4 years ago. Direct link to joseline.ramirez's post “can u make an example mo...”
can u make an example more easier
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- Kim Seidel
  Posted 4 years ago. Direct link to Kim Seidel's post “The example in the video ...”
  The example in the video is about as simple as it gets. Neither equation has fractions or decimals.
  
  The video is show you how to determine if an ordered pair (a point) is a solution to a system of equation. Sal has one point that he is testing to see if it is a solution to the system. In order for this to be true, the point must work in both equations (i.e., the 2 sides of each equation come out equal). He does the test by substituting the values from the ordered pair into each equation and simplifying.
  -- The point works in the 1st equation.
  -- The point did not work in the 2nd equation.
  This tells us the point in on the line created by the first equation, but it is not a point on the line created by the 2nd equation. Remember, to be solution to the system, the point must work for both equations. Since it didn't, the point is not a solution to the system.
  
  Hope this helps.
  Button navigates to signup page
  (7 votes)
sophia gonzalez
Posted 4 years ago. Direct link to sophia gonzalez's post “i dont understand math im...”
i dont understand math im confused
Button navigates to signup pageComment on sophia gonzalez's post “i dont understand math im...”
(7 votes)
Answer
- Derek Mayson
  Posted 16 days ago. Direct link to Derek Mayson's post “Math uses knowlegde to pe...”
  Math uses knowlegde to percilcoly explain how to solve problems
  Button navigates to signup page
  (1 vote)
𝓜𝓪𝓱𝓮𝓼𝓱 𝓜𝓪𝓱𝓮𝓷𝓭𝓻𝓪𝓴𝓪𝓻
Posted 4 years ago. Direct link to 𝓜𝓪𝓱𝓮𝓼𝓱 𝓜𝓪𝓱𝓮𝓷𝓭𝓻𝓪𝓴𝓪𝓻's post “*What does a system mean ...”
What does a system mean here?
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- David Severin
  Posted 4 years ago. Direct link to David Severin's post “A system of equations jus...”
  A system of equations just means at least 2 equations. For a single solution in a system of equations, you need as many independent equations as you have variables.
  Button navigates to signup page
  (5 votes)

Video transcript

Is negative 1 comma 7 a solution for the system of linear equations below? And they give us the first equation is x plus 2y is equal to 13. Second equation is 3x minus y is equal to negative 11. In order for negative 1 comma 7 to be a solution for the system, it needs to satisfy both equations. Or another way of thinking about it, x equals 7, and y-- sorry, x is equal to negative 1. This is the x coordinate. X equals negative 1, and y is equal to 7, need to satisfy both of these equations in order for it to be a Solution. So let's try it out. Let's try it out with the first equation. So we have x plus 2y is equal to 13. So if we're thinking about that, we're testing to see if when x is equal to negative 1, and y is equal to 7, will x plus 2y equals 13? So we have negative 1 plus 2 times 7-- y should be 7-- this needs to be equal to 13. And I'll put a question mark there because we don't know whether it does. So this is the same thing as negative 1 plus 2 times 7 plus 14. That does, indeed, equal 13. Negative 1 plus 14, this is 13. So 13 does definitely equal 13. So this point it does, at least, satisfy this first equation. This point does sit on the graph of this first equation, or on the line of this first equation. Now let's look at the second equation. I'll do that one in blue. We have 3 times negative 1 minus y, so minus 7, needs to be equal to negative 11. I'll put a question mark here because we don't know whether it's true or not. So let's see, we have 3 times negative 1 is negative 3. And then we have minus 7 needs to be equal to negative 11-- I put the question mark there. Negative 3 minus 7, that's negative 10. So we get negative 10 equaling negative 11. No, negative 10 does not equal a negative 11. So x equaling negative 1, and y equaling 7 does not satisfy the second equation. So it does not sit on its graph. So this over here is not a solution for the system. So the answer is no. It satisfies the first equation, but it doesn't satisfy the second. In order to be a solution for the system, it has to satisfy both equations.