Question

Solve the following equations using Graphical method:

$4x=y-5;y=2x+1$

Then $(x,y)$ is equal to

• A. $(-4,-2)$
• B. $(6,-2)$
• C. $(0,-4)$
• D. $(-2,-3)$

Answer 1

The correct option is D $(-2,-3)$

Writing both the equation as intercept form,

$\frac{x}{a}+\frac{y}{b}=1$

$4x=y-5$

$-4x+y=5$

$\Rightarrow \frac{x}{-\frac{5}{4}}+\frac{y}{5}=1$

$x$ axis intercept $=$ $-\frac{5}{4}$

$y$ axis intercept $=5$

Now $y=2x+1$

$-2x+y=1$

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

$x$ axis intercept $=$ $-\frac{1}{2}$

$y$ axis intercept $=1$

Drawing both the graphs, we get the following graphs
$-2x+y=1⟹$ black line
$-4x+y=5⟹$ brown line.

From the point of contact of both the lines, we get the value of $x$ and $y$

$x=-2$ and $y=-3$

Answer is $(-2,-3)$.