3y + x = -4, 3y - 4x = 6

Question

Elimination method

Answer 1

From the first equation, x=-4-3y, so we can substitute for x in the second equation:

3y-4(-4-3y)=6, 3y+16+12y=6, 15y=-10, y=-⅔. So x=-4-3y=-4+2=-2.

Another way:

3y+x=-4

3y-4x=6

Subtract the second equation from the first:

5x=-10, x=-2. Therefore 3y+x=3y-2=-4, 3y=-2, y=-⅔.

SOLUTION: x=-2, y=-⅔.

Either way eliminates one variable and allows calculation of the other.