Question

please someone help me out with this question:Determine the number of solutions for the linear system of equations below:

Answer 1

The Solution:

Given the system of equations below:

`\begin{gathered} y=-4x-2 \\ y=-4x+7 \end{gathered}`

We are required to determine the number of solutions for the given linear system.

Parallel Lines: If the two linear equations have the same slope (and different y-intercepts), the lines will be parallel. Since parallel lines never intersect, a system made up of two parallel lines will have NO solution since there is no intersection of the lines.

Equating both equations, we have:

`\begin{gathered} -4x-2=-4x+7 \\ \text{Collecting the like terms, we get} \end{gathered}`
`\begin{gathered} -4x+4x=7+2 \\ 0=9 \end{gathered}`

This means that there is NO SOLUTION for the two equations.