Question

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

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

Short answer

The system of equations have no solution

Step-by-step solution

Step 1. Given Information 

The given equations are

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

Step 2. Calculation    

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

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

Since $0\ne 1$is a false statement, the system of equations are inconsistent. The graph of these two equations would be the parallel line. Thus the system of the linear equation has no solution.