Question

Solve the following pairs of equations, graphically:

$3x-4y=1$ and $x-2y+1=0$

• A. $(-3,-2)$
• B. $(-3,2)$
• C. $(3,-2)$
  
• D. $(3,2)$

Answer 1

Answer: (D)

$(3,2)$

The solution set of equation $3x-4y=1$ is as follows:

If $x=-1$ then

$3\times (-1)-4y=1\Rightarrow -3-4y=1\Rightarrow -4y=1+3\Rightarrow -4y=4\Rightarrow y=-1$

If $x=3$ then

$3\times \left(3\right)-4y=1\Rightarrow 9-4y=1\Rightarrow -4y=1-9\Rightarrow -4y=-8\Rightarrow y=2$

The required points are $(-1,-1),(3,2)$.

Also, the solution set of equation $x-2y+1=0$ or $x-2y=-1$ is as follows:

If $x=1$ then

$1-2y=-1\Rightarrow -2y=-1-1\Rightarrow -2y=-2\Rightarrow y=1$

If $x=3$ then

$3-2y=-1\Rightarrow -2y=-1-3\Rightarrow -2y=--4\Rightarrow y=2$

The required points are $(1,1),(3,2)$.

Plot all the above points in the graph. Since the point of intersection in the graph is $(3,2)$.

Hence the solution is $x=3,y=2$.