Question

Solve each system by elimination. 2x + 3y = 125x - y =13Write the solution as an ordered pair (x,y)

Answer 1

`\begin{gathered} _{\text{ }}Let\colon \\ \begin{cases}2x+3y=12_{\text{ }}(1) \\ 5x-y=13_{\text{ }}(2)\end{cases} \end{gathered}`

Using elimination:

`\begin{gathered} (1)+3(2) \\ 2x+15x+3y-3y=12+39 \\ 17x=51 \\ x=(51)/(17) \\ x=3 \end{gathered}`

Replace x into (2):

`\begin{gathered} 5(3)-y=13 \\ 15-y=13 \\ y=15-13 \\ y=2 \end{gathered}`

Answer:

(3,2)