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:

$\begin{gathered} 17y=17 \\ \frac{17y}{17}=\frac{17}{17} \\ y=1 \end{gathered}$

Substitute y = 1 in the first equation:

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

Ans solve for x:

$\begin{gathered} 2x+3-3=9-3 \\ 2x=6 \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}$

Answer:

x = 3

y = 1