Question

Solve graphically, the following pair of linear equations:

$2x+y=23$
$4x-y=19$

• A. $x=1,y=4$
• B. $x=9,y=2$
• C. $x=5,y=0$
• D. $x=7,y=9$

Answer 1

Answer: (D)

$x=7,y=9$

The solution set of equation $2x+y=23$ is as follows:

If $x=5$ then

$2\times 5+y=23\Rightarrow 10+y=23\Rightarrow y=23-10\Rightarrow y=13$

If $x=7$ then

$2\times 7+y=23\Rightarrow 14+y=23\Rightarrow y=23-14\Rightarrow y=9$

The required points are $(5,13),(7,9)$.

Also, the solution set of equation $4x-y=19$ is as follows:

If $x=5$ then

$4\times 5-y=19\Rightarrow 20-y=19\Rightarrow -y=19-20\Rightarrow y=1$

If $x=7$ then

$4\times 7-y=19\Rightarrow 28-y=19\Rightarrow -y=19-28\Rightarrow y=9$

The required points are $(5,1),(7,9)$.

Plot all the above points in the graph. Since the point of intersection in the graph is $(7,9)$.

Hence the solution is $x=7,y=9$.