Question

Solve each system of equations by the substitution method.

$\begin{array}{c}4x-5y=92\\ x=7y\end{array}$

Short answer

The solution of the given system of equations is $x=28$, $y=4$.

Step-by-step solution

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

Substitute 7y for x into$4x-5y=92$ and simplify.

$\begin{array}{c}4\left(7y\right)-5y=92\\ 28y-5y=92\\ 23y=92\end{array}$

Step 2. Solve for one variable.

Divide each side of the equation obtained in step 1 by 23 to find the value of y.

$\begin{array}{c}\frac{23y}{23}=\frac{92}{23}\\ y=4\end{array}$

Step 3. Solve for another variable.

Substitute 4 for y into $x=7y$, to find the value of x.

$\begin{array}{c}x=7\times 4\\ =28\end{array}$

Therefore, the solution of the given system of equations is $x=28$, $y=4$.