Question

X = y - 4-2x + 3y= 6Solve each system by equation

Answer 1

Answer: x=-6 and y=-2

Given:

`\begin{gathered} x=y-4 \\ -2x+3y=6 \end{gathered}`

Having these two equations, we can substitute the first equation with the second equation to solve for y:

`\begin{gathered} -2x+3y=6 \\ \end{gathered}`

Since the first equation says that x = y - 4,

`\begin{gathered} -2x+3y=6 \\ -2(y-4)+3y=6 \\ -2y+8+3y=6 \\ -2y+3y=6-8 \\ y=-2 \end{gathered}`

Then, we will substitute this y-value to the first equation to solve for x.

`\begin{gathered} x=y-4 \\ x=-2-4 \\ x=-6 \end{gathered}`

We now have the values x=-6 and y=-2. To check, let us substitute both values to the second equation

`\begin{gathered} -2x+3y=6 \\ -2(-6)+3(-2)=6 \\ 12-6=6 \\ 6=6 \end{gathered}`

Therefore, the answer is correct, and the answer is x=-6 and y=-2