Question

When solving the system below algebraically using the substitution method, which of the following could be an equation you could create to solve for y?A. -4(2y - 20) + 3y = 30B. -4(-2y + 20) + 3y = 30C. -2y + 20 = -3y + 30D. 4(x + 2y = 20

Answer 1

The goal of the substitution method is to eliminate one of the variables using one of the equations of the systems. We are told that we want to solve for y, that is, we should use one equation to eliminate the variable x.

Since the coefficient of x in the first equation is 1, we will use the first equation to eliminate x in the second equation. So, we have the first equation

`x+2y=20`

So, by subtracting 2y on both sides, we get

`x=20-2y`

which is equivalent to

`x=-2y+20`

So, if we replace this value of x in the second equation,w e get

`-4\cdot(-2y+20)+3y=30`

which corresponds to option B