Question

Solve the following system of equations graohically on the set of axes below.

Answer 1

To solve the system of equation graphically we need to plot each equation on the plane. First we notice that both equation are linear, which means that their graphs are lines; this also means that to graph them we just need two points for each equation. Let's graph the equations.

First equation: y=x-2

As we said we just need two points on the line, to get them we just need to give values to x (any values we want) and plug them in the equation to get y.

If x=0, then we have:

`\begin{gathered} y=0-2 \\ y=-2 \end{gathered}`

hence the line passes through the point (0,-2)

If x=1, then we have:

`\begin{gathered} y=1-2 \\ y=-1 \end{gathered}`

hence the line passes through the point (1,-1)

With this we conclude that the line passes through the points (0,-2) and (1,-1). Plotting this points on the plane and joining them with a straight line we have the graph of the first equation:

Second equation: y=-2x-5:

We follow the same procedure as with the first equation.

If x=0 we have:

`\begin{gathered} y=-2(0)-5 \\ y=-5 \end{gathered}`

Hence the line passes through (0,-5)

If x=1 we have:

`\begin{gathered} y=-2\left(1\right)-5 \\ y=-2-5 \\ y=-7 \end{gathered}`

Hence the line passes through (1,-7)

Plotting this points and joining then with a line we have the graph for the second equation:

Finally, we plot both lines in the same plane. The solution of the system will be the point of intersection of the lines. The graph of the system is shown below:

From it we notice that the lines intersect at (-1,-3).

Therefore, the solution of the system is the point (-1,-3) which means that x=-1 and y=-3.