Question

Consider the following system of equations.x - 5y = -94x + 4y = -12Step 1 of 2: Determine if the point (-4,1) lies on both of the lines in the system of equations by substituting theordered pair into both equations.

Answer 1

Remember that the coordinates of a point are given as (x,y).

In this case, to find if the point (-4,1) lies on each of the lines in the system of equations, replace x=-4 and y=1 to find if the equation is satisfied or not.

First equation:

`\begin{gathered} x-5y=-9 \\ \Rightarrow(-4)-5(1)=-9 \\ \Rightarrow-4-5=-9 \\ \Rightarrow-9=-9 \end{gathered}`

The equation is satisfied. Then, the point (-4,1) belongs to the first line.

Second equation:

`\begin{gathered} 4x+4y=-12 \\ \Rightarrow4(-4)+4(1)=-12 \\ \Rightarrow-16+4=-12 \\ \Rightarrow-12=-12 \end{gathered}`

The equation is satisfied. Then, the point (-4,1) belongs to the second line.

Since the point (-4,1) belongs to both lines, then it is a solution to the system of equations.