Question

Use elimination to solve each system of equations.

$\begin{array}{c}9x-24y=-6\\ 3x+4y=10\end{array}$

Short answer

The required solution is represented by $x=2$and .$y=1$

Step-by-step solution

Step 1. Number the provided equations.

Make consideration that,

$$\begin{gathered} 9x-24y=-6\mathrm{......}\left(1\right) \\ 3x+4y=10\mathrm{......}\left(2\right) \end{gathered}$$

Step 2. Make a third equation.

Take equation (2) and perform multiplication between it and 3.

$$\begin{gathered} 3\left(3x+4y\right)=3\left(10\right) \\ 9x+12y=30\mathrm{......}\left(3\right) \end{gathered}$$

Step 3. Perform subtraction of equation (3) from the equation (3) to get the value of y after it use the obtained value to get the value of x.

Perform subtraction of equation (1) from the equation (3) to extract the value of y.

$$\begin{gathered} \left(9x+12y\right)-\left(9x-24y\right)=30-\left(-6\right) \\ 9x+12y-9x+24y=30+6 \\ 36y=36 \\ y=\frac{36}{36} \\ y=1 \end{gathered}$$

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

$$\begin{gathered} 9x-24\left(1\right)=-6 \\ 9x-24=-6 \\ 9x=-6+24 \\ 9x=18 \\ x=\frac{18}{9} \\ x=2 \end{gathered}$$

Step 4. Write the conclusion.

The obtained value of x and y represents the required solution that is$x=2$ and $y=1$.