Question

Solve each of the following system of equations graphically:
$2x+3y-4=0$
$3x-y+5=0$

Answer 1

$2x+3y-4=0$....(1)
$3x-y+5=0$......(2)

Isolate $x$ from equation (1) and find the values of $x$ and $y$.
$2x+3y-4=0$
or $x=\frac{4-3y}{2}$

Hence,

$x:$	$2$	$-1$	$5$
$y:$	$0$	$2$	$-2$

Now, plot the points $(2,0),(-1,2)and(5,-2)$ on the graph to get the straight line represented by the equation $2x+3y-4=0$.

Similarly, isolate $x$ from equation (2) and find the values of $x$ and $y$.

$3x-y+5=0$
or $y=5+3x$

$x:$	$0$	$-1$	$-2$
$y:$	$5$	$2$	$-1$

Now, plot the points $(0,5),(-1,2)and(-2,-1)$ on the graph to get the straight line represented by the equation $3x-y+5=0$.

The graph of both the lines will be as shown in the figure given above.

We can see from the graph that, both the lines intersect each other at point $(-1,2)$.

So, $x=-1,y=2$ is the solution of the given system of equations.

Hence, $(-1,2)$ is the required solution.