Question

In the following exercises, solve the systems of equations by substitution.

$$\begin{gathered} y=-\frac{1}{4}x \\ x+4y=8 \end{gathered}$$

Short answer

The system of equations has no solution

Step-by-step solution

Step 1. Given Information 

The given equations are

$$\begin{gathered} y=-\frac{1}{4}x \\ x+4y=8 \end{gathered}$$

Step 2. Calculation 

Substitute the equation first in the second equation to find the value of variable x.

$$\begin{gathered} x+4y=8 \\ x+4\left(\frac{-1}{4}x\right)=8 \\ x-x=8 \\ 0\ne 8 \end{gathered}$$

Since $0\ne 8$is a false statement, the system of equations is inconsistent. The graph of these two equations would be the parallel line. Thus the system of the linear equation has no solution.