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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.

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  • blobby green style avatar for user sharon moyes
    why do you add 8?
    (4 votes)
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  • blobby green style avatar for user vancespringsteen
    Which ordered pair is on the graph of the equation 2x+5y=4??
    (4 votes)
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  • mr pink red style avatar for user kyler gardner
    what do ordered pairs have to do with the math in the real world i just don't get it?
    (4 votes)
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  • purple pi purple style avatar for user Syann.Minor
    How do you do linear equations with 0,0 as your ordered pair
    (2 votes)
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  • blobby green style avatar for user Shannon Sauer
    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)
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    • piceratops ultimate style avatar for user Just Keith
      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)
  • hopper cool style avatar for user Grant Hopkins
    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)
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    • hopper cool style avatar for user Chuck Towle
      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)
  • blobby green style avatar for user jts1girl
    Which ordered pair is not included in the graph of p=3m+6? (1,9) , (3,12) , (10,36) , (6,18)
    (1 vote)
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    • leaf orange style avatar for user Benny C
      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)
  • blobby green style avatar for user sexychocolate148
    When your typing out the ordered pair do you put the largest number first?
    (0 votes)
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  • hopper cool style avatar for user BoMAN
    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)
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    • piceratops seed style avatar for user Fizza Naqvi
      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)
  • hopper cool style avatar for user Athena Tian
    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)
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    • stelly blue style avatar for user Kim Seidel
      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.