Main content

## Algebra (all content)

### Unit 3: Lesson 1

Two-variable linear equations intro- Two-variable linear equations intro
- Solutions to 2-variable equations
- Worked example: solutions to 2-variable equations
- Solutions to 2-variable equations
- Completing solutions to 2-variable equations
- Complete solutions to 2-variable equations
- Solutions to 2-variable equations: substitution (old)
- Solutions to 2-variable equations: graphical (old)

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# Solutions to 2-variable equations: substitution (old)

An old video of Sal checking whether (3,-4) is a solution of 5x+2y=7 by substituting x=3 and y=-4. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- why do you add 8?(4 votes)
- you do not add 8 you actually subtract 8.

because when you plus a negative number, it is just like subtraction(1 vote)

- Which ordered pair is on the graph of the equation 2x+5y=4??(4 votes)
- There are an unlimited number of points on a line. To ask which ordered pair is on the line itself, you would have to give options.(2 votes)

- what do ordered pairs have to do with the math in the real world i just don't get it?(4 votes)
- How do you do linear equations with 0,0 as your ordered pair(2 votes)
- You just simply plug in (0,0) into the equation and get an answer(1 vote)

- Have a question about direct relationship in regards to chemistry and graphing them using y=kx. I don't understand it?? Please help!(2 votes)
- Simply put a direct relationship between two variables is one in which if you divide one by the other you always get the same exact number for all non-zero values of the two variables.

An inverse relationship is one in which if you multiply the two variables you always get the same exact number for all non-zero values of the two variables.(1 vote)

- If you had and equation that wasn't in slope-intercept form, then would you have to put the equation in slope intercept form?(0 votes)
- Gropkins,

You do not have to put an equation in slope intercept form to graph the equation (unless that is the assignment).

As long as you are sure it is a linear equation, you graph the equation by finding any two points on the line and then plotting the two points and drawing a line through the points. You can find a point by choosing any value for x and finding the y value without putting the equations in slope y-intercept form. Choose a different value for x and find another point the same way.

But if the equation is put in slope y-intercept form, you can graph it by plotting the y-intercept and then using the slope to find a second point.

I hope that helps make it click for you.(5 votes)

- Which ordered pair is not included in the graph of p=3m+6? (1,9) , (3,12) , (10,36) , (6,18)(1 vote)
- I won't give the answer, but I'll tell you how to do it yourself. In this equation, p = y and m = x. So, with each of your ordered pairs, plug them into the equation and calculate it. If both sides are equal, the pair is included in the graph. If they aren't equal, then the pair is not in the graph.

For example, the first coordinate (1, 9).

9 = 3(1) + 6.

9 = 3 + 6

9 = 9

So (1, 9) is included in the graph.(2 votes)

- When your typing out the ordered pair do you put the largest number first?(0 votes)
- No. Ordered pairs are always (x, y). x always goes first and y always goes second. If you didn't put them in that order, then you wouldn't know which was which.(6 votes)

- Could someone explain to me how Sal got 5(3) + 2(-4) = 15+-8 = 7? Sal just wrote it down without explaining anything. Please Help!(0 votes)
- We had to find out whether (3,-4) is a solution of the equation 5x+2y=7.. In The ordered pair (3,-4) ..3 is the value of x and -4 is the value of y.. So subsituting the values of x and y in the equation as..

5(3) + 2(-4)=7 we get the answer.. If you still have any questions then fire away..(2 votes)

- I dont exactly get it. Does solution mean equal? I dont think Sal completely explained it that well. Can someone explain please and thank you?(1 vote)
- A linear equation like shown in the video will create a straight line when graphed. Every point on this line is a solution to the equation. Each point is defined by an ordered pair (x, y). If you substitute the ordered pair into the equation, it will make the 2 sides of the equation be equal to each other.

Hope this helps.(2 votes)

## Video transcript

Is 3 comma negative 4 a
solution to the equation 5x plus 2y is equal to 7? So they're saying, does x
equal 3, y equal negative 4, satisfy this equation, or
this relationship right here? So one way to do it is just
to substitute x is equal to 3 and y equals
negative 4 into this and see if 5 times x plus 2
times y does indeed equal 7. So we have 5 times 3
plus 2 times negative 4. This is equal to 15. 15 plus negative 8, which
does indeed equal 7. So it does satisfy the equation. So it is on the line. It is a solution. x equals 3, y equals negative 4
is a solution to this equation. So we've essentially
answered our question. It is. Now, another way to
do it, and I'm not going to go into
the details here, is you could actually
graph the line. So maybe the line might
look something like this, I'm not going to
do it in detail. And you see, if you have
a very good drawing of it, you see whether the
point lies on the line. If the point, when you graph
the point, does lie on the line, it would be a solution. If the point somehow ends
up not being on the line then you'd know it
isn't a solution. But to do this, you would have
to have a very good drawing and so you could very
precisely determine whether it's on the line. If you do the
substitution method, if you just substitute the
values into the equation and see if it comes
out mathematically, this will always be exact. So this is all we really
had to do in this example. So it definitely is a
solution to the equation.