Question

B. Solve the system of linear equations y = x + 2 and y = 3x – 4 by graphing.

Answer 1

To find the solution we need to graph both lines on the plane. To do this we need to find two points for each line.

First we graph the line y=x+2. To find a point we give x a value, whichever value we like, and then find y.

Let x=0, then:

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

Then we have the point (0,2).

Let x=1, then:

`\begin{gathered} y=1+2 \\ y=3 \end{gathered}`

Then we have the point (1,3).

Then we plot this points in the plane and join them with a line:

Now let's plot eh second line, y=3x-4.

Let x=0, then:

`\begin{gathered} y=3(0)-4 \\ y=-4 \end{gathered}`

So we have the points (0,-4).

Let x=1, then:

`\begin{gathered} y=3(1)-4 \\ y=3-4 \\ y=-1 \end{gathered}`

so we have the point (1,-1).

Now we plot this points and join them with a line:

Once we have both lines graph in the plane the solution is the intersection of the lines. Looking at the graph we conclude that the solution of the system is x=3 and y=5.