Question

Use substitution to solve each system of equations.

$$\begin{gathered} y=-2x-3 \\ x+y=9 \end{gathered}$$

Short answer

The required solution is represented by $x=-12$and $y=21$.

Step-by-step solution

Step 1. Number the provided equations.

Make consideration that,

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

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.

$$\begin{gathered} x+\left(-2x-3\right)=9 \\ -x-3=9 \\ -x=9+3 \\ x=-12 \end{gathered}$$

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

$$\begin{gathered} y=-2\left(-12\right)-3 \\ =24-3 \\ =21 \end{gathered}$$

Step 3. Write the conclusion.

The obtained value of x and y represents the required solution that is $x=-12$, and $y=21$.