Question

This is confusing, please explain how best to solve it. Thanks

Answer 1

To solve a system of equations using the substitution method

We use one equation to find x in terms of y, then

Substitute x in the second equation by the result of the first step

Since the given system is

`\begin{gathered} x-4y=20\rightarrow(1) \\ -2x+2y=-16\rightarrow(2) \end{gathered}`

We will add equation (1) by 4y (each side) to find x in terms of y

`\begin{gathered} x-4y+4y=20+4y \\ x=20+4y\rightarrow(3) \end{gathered}`

Now, substitute x in equation (2) by equation (3)

`-2(20+4y)+2y=-16`

Simplify the left side

`\begin{gathered} -2(20)-2(4y)+2y=-16 \\ -40-8y+2y=-16 \end{gathered}`

Add the like terms on the left side

`\begin{gathered} -40+(-8y+2y)=-16 \\ -40+(-6y)=-16 \\ -40-6y=-16 \end{gathered}`

Add 40 to each side

`\begin{gathered} -40+40-6y=-16+40 \\ -6y=24 \end{gathered}`

Divide both sides by -6 to find y

`\begin{gathered} (-6y)/(-6)=(24)/(-6) \\ y=-4 \end{gathered}`

Substitute y in equation (3) by -4

`\begin{gathered} x=20+4(-4) \\ x=20+(-16) \\ x=20-16 \\ x=4 \end{gathered}`

The answer is (x, y) = (4, -4)

x = 4

y = -4