Question

Solve each system of equations by the substitution method.

$\begin{array}{c}y=3x\\ 5x+y=24\end{array}$

Short answer

The solution of given system of equations is $x=3$, $y=9$.

Step-by-step solution

Step 1. Substitute value of one variable from one equation to another.

Substitute $3x$ for y into $5x+y=24$and simplify.

$\begin{array}{c}5x+3x=24\\ 8x=24\end{array}$

Step 2. Solve for one variable.

Divide each side of the equation obtained in step 1 by 8 to find the value of x.

$\begin{array}{c}\frac{8x}{8}=\frac{24}{8}\\ x=3\end{array}$

Step 3. Solve for another variable.

Substitute 3 for x into $y=3x$, to find the value ofy.
$\begin{array}{c}y=3\times 3\\ =9\end{array}$

Therefore, the solution of given system of equations is $x=3$, $y=9$.