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How to solve x+y=8 and 2x+y=11 using substitution

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2 Answers

You have a choice whether you want to substitute for x or y.  I look at both equations and I notice that the second one has 2x + y, so it might be easier to substitute for y.

In the first equation, let's solve for y.     x + y = 8, subtract x from both sides

                                                               y = 8-x

Now in the second equation, use (8-x) in place of y: 2x + y =11, so 2x + (8-x) = 11

Solve for x.  2x -x + 8 =11   Combine x terms

                         x+8 = 11, subtract 8 both sides.

                             x = 3

Now that you know x =3, substitute that in for x in either equation and solve for y. Once you know BOTH x and y, you have the solution.  The coordinate (x,y) represents where the 2 lines will intersect.

Looking at the equation, x+y=8, I can subtract either x or y from both sides to get the following two equations:

x = 8 - y,     or    y = 8 - x.

So I now have an expression which I can substitute for either x or y.

Now, looking at the equation, 2x + y = 11, I can substitute either way:

    2x + y = 11                                                              2x + y = 11

   2 (8 - y) + y = 11                                                      2x + (8 - x) = 11

   16 - 2y + y = 11                                                       2x + 8 - x = 11

   -2y + y = 11 - 16                                                     2x - x = 11 - 8

   -y = -5   therefore y = 5                                                  x = 3

    Now, to check our work:   x + y = 3 + 5 = 8

                                and:  2x + y  = (2 * 3) + 5 = 6 + 5 = 11.

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