Solve linear equations using substitution

Question

-4x-2y=-2

-8x+5y=5

Answer 1

We will need to solve one of the equations for one of the variables. I am choosing to solve the top equation for y.

-4x - 2y = -2

And 4x to both sides

-2y = 4x - 2

Divide both sides by -2

y = -2x + 1

This can now be substitute into the BOTTOM equation, to replace the "y" in 5y.

-8x + 5 (-2x + 1) = 5

Distribute the 5 into the parentheses.

-8x -10x + 5 = 5

Combine like terms on the left side.

-18x + 5 = 5

Subtract 5 from both sides

-18x = 0

Divide both sides by -18

and get x = 0

Put this x back into one of the original equations to find y.

Into the top equation we get -4(0) -2y = -2, this is 0 - 2y = -2 which is

-2y = -2

Divide both sides by -2 and get

y = 1

Then check x=0, y=1 in the bottom equation to be sure this solution works there also:

-8(0) + 5(1) = 0 + 5 = 5 YES, it works. So our answer is (0,1) represented as a point, or as a list:

x = 0, y = 1