help on translation?

Question

Solve the following system of linear equations by the addition method. If there is no solution or an infinite number of solutions, so state. Check your answer.
4x + 3y = 12
2x – 4y = 6


so far:
x=3(-y+4)/4
y=4(-x+3)/3

am I close yet?

Answer 1

This is the addition method, but your doing it the substitution method, so according to the problem you are wrong.

You need to make one of the variables cancel out, so multiply the second equation by -2. You get:

4x + 3y = 12
-4x + 8y = -12

Now add. You get:

0x + 11 y = 0
11y = 0
y = 0

Now plug this in one of the equations.

4x + 3(0) = 12
4x + 0 =12
4x = 12
x = 3

You can check this with the other one also.

2x - 4(0) = 6
2x - 0 = 6
2x = 6
x = 3

So x = 3, y = 0

Answer 2

-2(2x - 4y) = -2 * 6 >> -4x + 8y = -12

4x + 3y = 12
-4x + 8y = -12
____________

0 + 11y = 0 >> y = 0 ; substituting

4x = 12 >> x = 3 //

confirming:

2x = 6 >> x = 3

Hope to have helped. It was fun!