Question

Solve each System of equations by graphing.Y=2x -5Y= -x -2

Answer 1

Given:

`\begin{gathered} y=2x-5 \\ y=-x-2 \end{gathered}`

To plot the two equations on a line, we need to get at least two points to plot the line.

Using the x and y-intercepts as the two points,

For the line y = 2x - 5,

`\begin{gathered} y=2x-5 \\ \text{when x = 0,} \\ y=2(0)-5 \\ y=0-5 \\ y=-5 \\ \text{Hence, the point is (0,-5)} \\ \\ \text{Also, when y = 0,} \\ 0=2x-5 \\ 0+5=2x \\ 5=2x \\ (5)/(2)=x \\ x=2.5 \\ \text{Hence, the second point is (2.5,0)} \end{gathered}`

For the line y = -x - 2,

`\begin{gathered} y=-x-2 \\ \text{when x = 0,} \\ y=-0-2 \\ y=-2 \\ \text{Hence, the point is (0,-2)} \\ \\ \text{Also, when y = 0,} \\ 0=-x-2 \\ 0+x=-2 \\ x=-2 \\ \text{Hence, the second point is (-2,0)} \end{gathered}`

Using the points gotten for both equations, the lines can be plotted as shown below;

The solution to the system of equations is the point where both lines intersect.

The point of intersection of both lines from the graph is at (1,-3)

Therefore, the solution to the system of equations is (1,-3)