Question

Use substitution to solve each system of equations.

$$\begin{gathered} y=x+4 \\ 2x+y=16 \end{gathered}$$

Short answer

The required solution is represented by $x=4$and $y=7$.

Step-by-step solution

Step 1. Number the provided equations.

Make consideration that,

$\begin{array}{l}y=x+4\mathrm{......}\left(1\right)\\ 2x+y=16\mathrm{......}\left(2\right)\end{array}$

Step 2. Take the help of equation (1) to get the value of x after it use the obtained value to get the value of y. 

The equation (1) is representing the value of y in the form of an expression so use it for the equation (2) to extract the value of x.

$$\begin{gathered} 2x+\left(x+4\right)=16 \\ 3x+4=16 \\ 3x=16-4 \\ x=\frac{12}{3} \\ x=4 \end{gathered}$$

Use the obtained value of x into equation (1) to get the value of y.

$$\begin{gathered} y=3+4 \\ =7 \end{gathered}$$

Step 3. Write the conclusion.

The obtained value of x and y represents the required solution that is$x=4$ and $y=7$.