Question

Use elimination to solve eachsystem of equations2x + 3y = 9 8x - 5y = 19

Answer 1

Multiply the first equation by 4:

`\begin{gathered} 4(2x+3y=9) \\ 8x+12y=36 \end{gathered}`

Subtract the second equation:

`\begin{gathered} 8x+12y=36 \\ - \\ 8x-5y=19 \end{gathered}`

This is:

`\begin{gathered} 8x+12y-(8x-5y)=36-19 \\ 8x+12y-8x+5y=17 \end{gathered}`

Simplify:

`\begin{gathered} 17y=17 \\ (17y)/(17)=(17)/(17) \\ y=1 \end{gathered}`

Substitute y = 1 in the first equation:

`\begin{gathered} 2x+3(1)=9 \\ 2x+3=9 \end{gathered}`

Ans solve for x:

`\begin{gathered} 2x+3-3=9-3 \\ 2x=6 \\ (2x)/(2)=(6)/(2) \\ x=3 \end{gathered}`

Answer:

x = 3

y = 1