Question

Use the elimination to solve each system of equations exercise number 4)

Answer 1

To solve this system of linear equations using the elimination method, first, add both equations:

`\begin{gathered} 8x+5y=38\Rightarrow\text{ Equation 1} \\ -8x+2y=4\Rightarrow\text{ Equation 2} \end{gathered}`
`\begin{gathered} 8x+5y=38 \\ -8x+2y=4\text{ +} \\ --------- \\ 0x+7y=42 \\ 7y=42 \end{gathered}`

Now solve for y dividing by 7 on both sides of the equation:

`\begin{gathered} (7y)/(7)=(42)/(7) \\ y=6 \end{gathered}`

Finally, replace the value of y in any of the initial equations, for example in equation 1

`\begin{gathered} 8x+5y=38 \\ 8x+5(6)=38 \\ 8x+30=38 \\ \text{ Subtract 30 from both sides of the equation} \\ 8x+30-30=38-30 \\ 8x=8 \\ \text{ Divide by 8 from both sides of the equation} \\ (8x)/(8)=(8)/(8) \\ x=1 \end{gathered}`

Therefore, the solution of the system of equations is

`\begin{cases}x=1 \\ y=6\end{cases}`