Question

Solve each system of equations by the substitution method.

$$\begin{gathered} 3x+2y=71 \\ y=4+2x \end{gathered}$$

Short answer

The solution of a given system of equations is $x=9$, $y=22$.

Step-by-step solution

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

Substitute$4+2x$ for y into$3x+2y=71$ and simplify.

$$\begin{gathered} 3x+2\left(4+2x\right)=71 \\ 3x+8+4x=71 \\ 7x+8=71 \end{gathered}$$

Step 2. Solve for one variable.

Subtract 8 from both the sides of the equation obtained in step 1 and simplify.

$$\begin{gathered} 7x+8-8=71-8 \\ 7x=63 \end{gathered}$$

Divide each side of the equation obtained in step 2 by 7 to find the value of x.

$\begin{array}{c}\frac{7x}{7}=\frac{63}{7}\\ x=9\end{array}$

Step 3. Solve for another variable.

Substitute 9 for x into $y=4+2x$, to find the value of y.

$$\begin{gathered} y=4+2\times 9 \\ =4+18 \\ =22 \end{gathered}$$

Therefore, the solution of given system of equations is $x=9$, $y=22$.