Question

Solve the linear system using the elimination method. Type youranswer as an ordered pair in the form (#,#).3x - y = 20-8x + 7y = -49

Answer 1

$\begin{gathered} 3x-y=20 \\ -8x+7y=-49 \end{gathered}$

to use elimination method need the same variable with the same number

i will multiply the first equation by 7 and then sum with the secont equation to eliminate y

$\begin{gathered} 3x(7)-y(7)=20(7) \\ 21x-7y=140 \\ \end{gathered}$

now we do the sum

$\begin{gathered} 21x-7y=140+ \\ -8x+7y=-49 \\ -------------- \\ 13x+0y=91 \end{gathered}$

we can solve x from that equation

$\begin{gathered} 13x=91 \\ x=\frac{91}{13}=7 \end{gathered}$

now we can use x=7 to replace on any equation and solve y (I will use the first equation)

$\begin{gathered} 3(7)-y=20 \\ 21-y=20 \\ y=1 \end{gathered}$

the ordered pair of the solution is (7,1)