Question

Solve the following pairs of equations, graphically:

$\frac{x}{2}-\frac{y}{3}=3$ and $x+y=1$

• A. $(-4,3)$
• B. $(4,-3)$
• C. $(-4,-3)$
• D. $(4,3)$

Answer 1

The correct option is B $(4,-3)$

The solution set of equation $\frac{x}{2}-\frac{y}{3}=3$ or $3x-2y=18$ is as follows:

If $x=0$ then

$3\times 0-2y=18\Rightarrow -2y=18\Rightarrow y=-9$

If $x=4$ then

$3\times 4-2y=18\Rightarrow 12-2y=18\Rightarrow y=-3$

The required points are $(0,-9),(4,-3)$.

Also, the solution set of equation $x+y=1$ is as follows:

If $x=0$ then

$0+y=1\Rightarrow y=1$

If $x=4$ then

$4+y=1\Rightarrow y=1-4=-3$

The required points are $(0,1),(4,-3)$.

Plot all the above points in the graph. Since the point of intersection in the graph is $(4,-3)$.

Hence the solution is $x=4,y=-3$.