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Worked example: solutions to 2-variable equations

How do you check if an ordered pair is a solution to a given equation? You need to plug in the numbers and see what equality results. Watch this video to see a worked example.

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  • blobby green style avatar for user Adam H.
    At , would the equation y = -2+ 4/3y be equivalent?
    (14 votes)
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  • piceratops seed style avatar for user lhauck
    what if you are not given an ordered pair and you have to figure out this equation
    (6 votes)
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  • leafers seedling style avatar for user David Pineda
    does this cover absolute vale equalities and inequalities
    (3 votes)
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    • aqualine ultimate style avatar for user atrew1
      I saw nothing here about absolute values which would look like "|x|" or |3|=3 or |-3|=3 OR |-9|=9
      The best way to think about absolute values is- "No matter the sign (+ or -) the number remains positive, because the absolute value cannot be negative" Hope that helps. Now inequalities, something simple like....... 1<x<3 where "x" is greater then 1 but less then 3.. The interval notation would be (SET BUILDER NOTATION!)----> {x|x>1, x<3} or (INTERVAL NOTATION(WHICH IS INCLUDING A UNION aka "U"))--> (1,x)U(x,3)...... if the sign was a "greater than or equal to, or less than or equal to" then the interval notation would be [1,x]U[x,3].... I hope this helps.
      (8 votes)
  • starky sapling style avatar for user Azizbek
    What is an "ordered" pair?
    (2 votes)
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  • duskpin ultimate style avatar for user aj
    can't you simplify the equation first? like 4x + 3y = 6?
    (3 votes)
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  • blobby green style avatar for user Stephanie Gaines
    solve the following systems of linear equations by elimination
    12x+5y=23
    2x-7y=39
    (4 votes)
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    • blobby green style avatar for user Hamid Dzzz
      Add two times the first equation to the second equation to eliminate x:

      12x + 5y = 23
      2x - 7y = 39

      (12x + 5y) + 2(2x - 7y) = 23 + 2 * 39

      26x - 18y = 101

      So, y = (26x - 101) / -18. Substitute the expression for y back into the first equation to solve for x:

      12x + 5y = 23

      12x + 5((26x - 101) / -18) = 23

      Expand the right side and simplify:

      12x + (130x - 505) / -18 = 23

      -6x - 505 / -18 = 23

      Multiply both sides by -18 to get rid of the fraction:

      6x + 505 = -414

      Subtract 505 from both sides to isolate x:

      6x = -919

      Divide both sides by 6 to find x:

      x = -153

      Finally, substitute the value of x back into the expression for y:

      y = (26x - 101) / -18

      y = (26 * -153 - 101) / -18

      y = 24.

      The solution is x = -153 and y = 24.
      (2 votes)
  • hopper cool style avatar for user Katherine Davis
    So my math book says that I should rewrite the equation first, simplify it, then graph it. how do I rewrite it? I keep trying and I keep getting the wrong answer.
    P.s. It gives me stuff like, 4X + Y = 6
    (4 votes)
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    • mr pink green style avatar for user David Severin
      rewriting for graphing purposes usually means to put in slope intercept form (isolate the y).
      Example: 4x + 3y = 9. Subtract 4x to get 3y=-4x+9
      Divide all by 3 to get 3/3 y= -4/3 x + 9/3, reduce to get y=-4/3 x + 3. Graph y intercept at (0,3), go down 4 right 3 to get to point (3,-1).
      (1 vote)
  • duskpin sapling style avatar for user 5 Miller, Ben
    I must be missing something that was already said, or something I don't know. But if the equation is like y = -2x - 5. Could you still be able to do what he is doing in the video? I feel like you can but how?
    (2 votes)
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    • stelly blue style avatar for user Kim Seidel
      You can! Anytime you are asked to determine if a point (an ordered pair of (x,y)) is a solution, we use substitution. We use the x-value for "x" in the equation and the y-value for "y" in the equation.

      Example: Is (2, 3) a solution to your equation: y = -2x - 5?
      Substitute: 3 = -2(2) - 5
      Simplify the right side:
      3 = -4 - 5
      3 = -9
      Since these are not equal, we know the point (2,3) is not a solution to this equation. Or, is not a point on the line that is created from this equation.

      If the 2 sides turn out to be equal, then you know the point is a solution to the equation.
      Hope this helps.
      (5 votes)
  • winston baby style avatar for user Zakary
    where did this dude go to school. Mans smart
    (4 votes)
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  • piceratops ultimate style avatar for user Leonardo Padro
    Is there an easy way to narrow down the answer besides go through each answer one by one? If so what is it?
    (1 vote)
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Video transcript

- [Voiceover] "Which of the ordered pairs is a "solution of the following equation?" 4x minus one is equal to 3y plus five. Now, when we look at an ordered pair we wanna figure out whether it's a solution, we just have to remind ourselves that in these ordered pairs the convention, the standard, is is that the first coordinate is the x coordinate, and the second coordinate is the y coordinate. So they're gonna, if this is a solution, if this ordered pair is a solution, that means that if x is equal to three and y is equal to two, that that would satisfy this equation up here. So let's try that out. So, we have four times x. Well we're saying x needs to be equal to three, minus one, is going to be equal to three times y. Well, if this ordered pair is a solution then y is going to be equal to two, so three times y, y is two, plus five. Notice all I did is wherever I saw the x, I substituted it with three, wherever I saw the y, I substituted it with two. Now let's see if this is true. Four times three is twelve, minus one. Is this really the same thing as three times two which is six, plus five? See, 12 minus one is 11, six plus five is also 11. This is true, 11 equals 11. This pair three, two does satisfy this equation. Now let's see whether this one does, two, three. So this is saying when x is equal to two, y would be equal to three for this equation. Let's see if that's true. So four times x, we're now gonna see if when x is two, y can be three. So four times x, four times two, minus one is equal to three times y, now y we're testing to see if it can be three. Three times three plus five, let's see if this is true. Four times two is eight, minus one, is this equal to three times three? So that's nine plus five. So is seven equal to 14? No, clearly seven is not equal to 14. So these things are not equal to each other. So this is not a solution, when x equals two y cannot be to three and satisfy this equation. So only three, two is a solution.