Question

Draw the graph of the equation 2x − 3y = 5. From the graph, find (i) the value of y when x = 4 and (ii) the value of x when y = 3.

Answer 1

Given equation :

$$\begin{gathered} 2x-3y=5 \\ \Rightarrow 2x=3y+5 \\ \Rightarrow x=\frac{3y+5}{2} \end{gathered}$$
When, $y=-1,x=\frac{-3+5}{2}=\frac{2}{2}=1$

When, $y=-3,x=\frac{-9+5}{2}=\frac{-4}{2}=-2$
Thus, we have the following table:

$\text{x}$	1	-2
$y$	-1	-3

Plot the points $(-2,-3),(1,-1)$ on the graph paper and extend the line in both directions.

(i) When x = 4:
$$\begin{gathered} 4=\frac{3y+5}{2}\Rightarrow 8=3y+5 \\ \Rightarrow 3y=8-5=3 \\ \Rightarrow 3y=3 \\ \Rightarrow y=1 \end{gathered}$$
(ii) When y = 3:
$x=\frac{3y+5}{2}=\frac{14}{2}=7$