Solve the system of equations:y=x+8x+y = 2

Question

asked Dec 16, 2023 8.3k views

2 Answers

Guy Dubrovski · Answer 1 · 2023-12-22T04:12:01+0000

We can solve the system of equations:

$\begin{gathered} y=x+8 \\ x+y=2 \end{gathered}$

by elimination method.

If we multiply the first equation by -1, we have the following equivalent system:

$\begin{gathered} -y=-x-8 \\ x+y=2 \end{gathered}$

If we add both equation, we obtain

because -y+y=0. Since -8+2=-6, we have

Now, we must move -x to the left hand side as +x. It yields,

$\begin{gathered} x+x=-6 \\ 2x=-6 \\ x=(-6)/(2) \\ x=-3 \end{gathered}$

Now, we can substitute this value into the first equation. It gives

$\begin{gathered} y=-3+8 \\ y=5 \end{gathered}$

Then, the answer is x=-3 and y=5.