Solve using the addition elimination methodStep By Step explanation please

Question

asked Jul 23, 2023 125k views

1 Answer

Locane · Answer 1 · 2023-07-27T15:18:33+0000

The 2 equations given,

$\begin{gathered} 2x+3y=6 \\ -7x-5y=1 \end{gathered}$

Let's multiply the first equation by "7" and the second equation by "2". We have,

$\begin{gathered} 7*\lbrack2x+3y=6\rbrack \\ 2*\lbrack-7x-5y=1\rbrack \\ ------------- \\ 14x+21y=42 \\ -14x-10y=2 \\ \end{gathered}$

Now we add both equations and solve for "y":

$\begin{gathered} 14x+21y=42 \\ -14x-10y=2 \\ ----------- \\ 11y=44 \\ y=(44)/(11) \\ y=4 \end{gathered}$

Now we substitute this value of y into the original first equation and solve for x:

$\begin{gathered} 2x+3y=6 \\ 2x+3(4)=6 \\ 2x+12=6 \\ 2x=6-12 \\ 2x=-6 \\ x=-(6)/(2) \\ x=-3 \end{gathered}$

So, the solution set is,