Answer
Solution: $(1,3)$
(checked below)
Work Step by Step
Step 1
Solve one of the equations for one of the variables.
Select the first equation as the x has a coefficient of -1.
$ 4y-x=5+2y\qquad$ ... add $x-5-2y$
$4y-2y-5=x$
$x=2y-5$
Step 2
Substitute $2y-5$ for $x$ in the other equation and solve for $y$
$ 3(2y-5)+7y=24\qquad$ ... (distribute, simplify)
$ 6y-15+7y=24\qquad$ ... add $15$, simplify
$ 13y=39\qquad$ ... divide with $13$
$y=3$
Step 3
Substitute $3$ for $y$ in $x=2y-5$.
$x=2(3)-5$
$x=1$
Solution: (x,y) = $(1,3)$
Check: $\left[\begin{array}{lll}
4(3)-1\stackrel{?}{=}5+2(3) & ..... & 3(1)+7(3)\stackrel{?}{=}24 \\
12-1=5+6 & & 3+21=24\\
11=11 & & 24=24\\
& &
\end{array}\right]$
