Question

Solve the system of equations by multiplying first. Enter the solutido as an ordered pair.< 6x+8y = 106The solution is the ordered pair

Answer 1

Let's solve the system

`\begin{cases}6x+8y=106 \\ 5x-4y=3\end{cases}`

First, multiply equation 2 by 2

`\begin{cases}6x+8y=106 \\ 5x-4y=3\end{cases}\rightarrow\begin{cases}6x+8y=106 \\ 10x-8y=6\end{cases}`

Then, add up equations 1 and 2

`\begin{cases}6x+8y=106 \\ 10x-8y=6\end{cases}\rightarrow16x=112`

Solve for x :

`16x=112\rightarrow x=(112)/(16)\Rightarrow x=7`

Substitute in equation 1 and solve for y :

`\begin{gathered} 6x+8y=106 \\ \rightarrow6(7)+8y=106 \\ \rightarrow8y=106-6(7) \\ \rightarrow8y=64\rightarrow y=(64)/(8)\Rightarrow y=8 \end{gathered}`

This way, we get that:

`\begin{gathered} x=7 \\ y=8 \end{gathered}`