Question

Draw the graphs of the equations 3x – 2y = 4 and x + y – 3 = 0. On the same graph paper, find the coordinates of the point were the two graph lines intersect.

Answer 1

$$\begin{gathered} 3x-2y=4 \\ \Rightarrow 2y=3x-4 \\ \Rightarrow y=\frac{3x-4}{2} \end{gathered}$$
When x = 0, $y=\frac{3\times 0-4}{2}=\frac{0-4}{2}=\frac{-4}{2}=-2$
When x = 2, $y=\frac{3\times 2-4}{2}=\frac{6-4}{2}=\frac{2}{2}=1$
When x = –2, $y=\frac{3\times \left(-2\right)-4}{2}=\frac{-6-4}{2}=\frac{-10}{2}=-5$
Thus, the points on the line 3x – 2y = 4 are as given in the following table:

x	0	2	–2
y	–2	1	–5

Plotting the points (0, –2), (2, 1) and (–2, –5) and drawing a line passing through these points, we obtain the graph of of the line 3x – 2y = 4.

$$\begin{gathered} x+y-3=0 \\ \Rightarrow y=-x+3 \end{gathered}$$
When x = 0, $y=-0+3=3$
When x = 1, $y=-1+3=2$
When x = –1, $y=-\left(-1\right)+3=1+3=4$
Thus, the points on the line x + y – 3 = 0 are as given in the following table:

x	0	1	–1
y	3	2	4

Plotting the points (0, 3), (1, 2) and (–1, 4) and drawing a line passing through these points, we obtain the graph of of the line x + y – 3 = 0.



It can be seen that the lines 3x – 2y = 4 and x + y – 3 = 0 intersect at the point (2, 1).