Solution:
Given:
[tex]\begin{gathered} y=2x-5 \\ y=-x-2 \end{gathered}[/tex]
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,
[tex]\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 \\ \frac{5}{2}=x \\ x=2.5 \\ \text{Hence, the second point is (2.5,0)} \end{gathered}[/tex]
For the line y = -x - 2,
[tex]\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}[/tex]
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)
