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Question from amber, a student:

Please help me with this problem
x+y=-2
y-2x=1

Hi Amber,

I'm going to illustrate with a different problem.

Solve the equations
y - x = 3
x + 2y = 3

I am going to use the substitution method so I want to solve one of the equations for one of the variables. I'm going to solve the first equation for y. If you add x to both sides of the first equation equation you get

y = x + 3

Now the substitution step, substitute y = x + 3 into the second equation

x + 2(x + 3) = 3

Now I have one equation in one unknown which I can solve

x + 2(x + 3) = 3
x + 2x + 6 = 3
3x + 6 = 3
3x = 3 - 6 = -3
x = -1.

To find y substitute x = -1 into either of the equations I started with. The first equation looks the easiest so

y - x = 3
y - (-1) = 3
y + 1 = 3
y = 3 - 1 = 2.

Thus my answer is x = -1, y = 2. (I checked by substituting these values into both equations to ensure that my answer was correct.)

Now use the same method to solve the equations you sent us.

Penny

 

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