Question

Use substitution to solve each system of equations.

$$\begin{gathered} y=-4x \\ 6x-y=30 \end{gathered}$$

Short answer

The required solution is represented by $x=3$and $y=-12$.

Step-by-step solution

Step 1. Number the provided equations.

Make consideration that,

$$\begin{gathered} y=-4x\mathrm{......}\left(1\right) \\ 6x-y=30\mathrm{......}\left(2\right) \end{gathered}$$

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.

$$\begin{gathered} 6x-\left(-4x\right)=30 \\ 6x+4x=30 \\ 10x=30 \\ x=\frac{30}{10} \\ =3 \end{gathered}$$

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

$\begin{array}{c}y=-4\cdot 3\\ =-12\end{array}$

Step 3. Write the conclusion.

The obtained value of x and y represents the required solution that is$x=3$ and $y=-12$.