Question

solve the following system of equations.

2x = 7+4y
4y + 3x = -2

Answer 1

2x - 4y = 7
3x + 4y = -2

Answer 2

x=7/2+2y
4y+2(7/2+2y)=-2
4y+7+4y=-2
8y=-2-7
8y=-9
8y/8=-9/8
y=-9/8

Answer 3

I'd start with Velvet's approach. Rearrange the first equation so that it is in standard form (ax + by = c) by subtracting 4y from each side.

2x - 4y = 7
3x + 4y = -2

Now, we want to combine them in a way that gets rid of one variable -- in this case, it's easy to get rid of y by adding the two equations together. (-4y + 4y = 0)

5x = 5
divide both sides by 5 to get
x=1

plug this in to either original equation, to get y:
2(1) = 7+4y
2 = 7 + 4y
-5=4y
-5/4 = y

check it by plugging out answers (1, -5/4) into the second equation:
3(1) + 4(-5/4) = -2
3 + (-20/4) = -2
3-5 = -2
-4y = 5

Answer 4

Didn't realize there's a length limit -- to finish:
y = -5/4

solution = (1, -5/4), which can be checked by plugging into the second equation.
3(1) + 4(-5/4) = -2, which it does