Question

Use elimination to solve each system of equations.

$$\begin{gathered} x+y=9 \\ x-y=-3 \end{gathered}$$

Short answer

The required solution is represented by $x=3$and $y=6$.

Step-by-step solution

Step 1. Number the provided equations.

Make consideration that,

$$\begin{gathered} x+y=9\mathrm{......}\left(1\right) \\ x-y=-3\mathrm{......}\left(2\right) \end{gathered}$$

Step 2. Perform addition between the provided equations to get the value of x after it use the obtained value to get the value of y.

Perform addition between the equation (1) and equation (2) to extract the value of x.

$$\begin{gathered} \left(x+y\right)+\left(x-y\right)=9+\left(-3\right) \\ x+y+x-y=6 \\ 2x=6 \\ x=\frac{6}{2} \\ x=3 \end{gathered}$$

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

$$\begin{gathered} 3+y=9 \\ y=9-3 \\ y=6 \end{gathered}$$

Step 3. Write the conclusion.

The obtained value of x and y represents the required solution that is$x=3$ and $y=6$.