Question

Solve the system of linear equations by elimination x+2y=13 -x+y=5

Answer 1

To solve the system

`\begin{gathered} x+2y=13 \\ -x+y=5 \end{gathered}`

we add the two equations to get:

`\begin{gathered} x+2y=13 \\ -x+y=5 \\ --------------_{} \\ 0+3y=18 \end{gathered}`

Dividing both sides by 3 gives

`y=6`

with the value of y in hand, we now put it in -x + y = 5 to get

`-x+6=5`

subtracting 6 from both sides gives

`-x=-1`
`x=1`

Hence, the solution to the system is

`\begin{gathered} x=1 \\ y=6. \end{gathered}`