91Ó°ÊÓ

Equation of line in slope intercept form is expressed below.

$y=mx+c$

Where m is the slope and c is the intercept of y-axis.

Consider the first equation $2x+3y=12$.

Rewrite the equation in form of slope-intercept form.

Subtract both sides by$2x$.

$\begin{array}{l}2x+3y−2x=12−2x\\ 3y=12−2x\end{array}$

Next, divide both sides by 3 and rearrange the terms.

$\begin{array}{l}\frac{3y}{3}=\frac{12−2x}{3}\\ y=\frac{12}{3}−\frac{2x}{3}\\ y=−\frac{2}{3}x+4\end{array}$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is $-\frac{2}{3}$ and intercept of y-axis c is $4$.

Now, consider the second equation $2x-y=4$.

Rewrite the equation in form of slope-intercept form.

Subtract both sides by$2x$

$\begin{array}{l}2x−y−2x=4−2x\\ −y=−2x+4\end{array}$

Multiply both sides by $-1$

$\begin{array}{l}y=2x−4\\ y=2x+(−4)\end{array}$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is$2$ and intercept of y-axis c is $-4$

Plot the equations on the same plane and the point where both the equations intersect is the solution of the system of the equations.

The red line denotes the equation$2x+3y=12$ and blue line denotes the equation $2x-y=4$.

Therefore, the point of intersection is$\left(3,2\right)$.

The point of intersection is solution of system of equations if the point satisfies both the equation.

Substitute the point $\left(3,2\right)$in the equation$2x+3y=12$.

Substitute x as 3 and y as $2$and check whether right hand side is equal to left hand side of the equation

$\begin{array}{l}2\left(3\right)+3\left(2\right)=12\\ 6+6=12\\ 12=12\end{array}$

Since, this is true so the point$\left(3,2\right)$satisfy the equation$2x+3y=12$.

Substitute the point $\left(3,2\right)$in the equation $2x-y=4$.

Substitute x as 3 and y as $2$and check whether right hand side is equal to left hand side of the equation

$\begin{array}{l}2\left(3\right)−2=4\\ 6−2=4\\ 4=4\end{array}$

Since, this is true so the point $\left(3,2\right)$ satisfy the equation $2x-y=4$.

Hence, the solution of the system of equations is $\left(3,2\right)$.