Answer
$a.$
Solution: ($\displaystyle \frac{22}{3},\ \displaystyle -\frac{43}{9} $)
$b.$
We solved the second equation for x,
as it was the only variable with a coefficient of $1$ or $-1.$
Work Step by Step
$a.$
Step 1
Solve one of the equations for one of the variables.
Select the second equation as the x has a coefficient of 1 next to it (easier path).
$ x+3y=-7\qquad$ ... subtract $-3y$
$x=-7-3y$
Step 2
Substitute $-7-3y$ for $x$ in the other equation and solve for $y$
$ 6y+5(-7-3y)=8\qquad$ ... simplify LHS (distribute)
$ 6y-35-15y=8\qquad$ ... add 35
$6y-15y=43$
$-9y=43\qquad $... divide with $(-9)$
$y=-\displaystyle \frac{43}{9}$
Step 3
Substitute $-\displaystyle \frac{43}{9}$ for $y$ in the equation obtained in step 1.
$x=-7-3(-\displaystyle \frac{43}{9})$
$x=-7+\displaystyle \frac{43}{3}=\frac{-21+43}{3}=\frac{22}{3}$
Write the solution as $(x,y).$
Solution: ($\displaystyle \frac{22}{3},\ \displaystyle -\frac{43}{9} $)
$b.$
We solved the second equation for x,
as it was the only variable with a coefficient of $1$ or $-1.$
