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 $3x-7y=-6$.

Rewrite the equation in form of slope-intercept form.

Subtract both sides by $3x$.

$\begin{array}{c}3x−7y−3x=−6−3x\\ −7y=−6−3x\end{array}$

Next, divide both sides by localid="1647363351911" $-7$and rearrange the terms.

$\begin{array}{c}\frac{−7y}{−7}=\frac{−6−3x}{−7}\\ y=\frac{6}{7}+\frac{3x}{7}\\ y=\frac{3}{7}x+\frac{6}{7}\end{array}$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is $\frac{3}{7}$ and intercept of y-axis c is $\frac{6}{7}$.

Now, consider the second equation $x+2y=11$.

Rewrite the equation in form of slope-intercept form.

Subtract both sides by x.

$\begin{array}{c}x+2y−x=11−x\\ 2y=11−x\end{array}$

Next, divide both sides by localid="1647363362422" $2$and rearrange the terms.

$\begin{array}{c}\frac{2y}{2}=\frac{11−x}{2}\\ y=\frac{11}{2}−\frac{x}{2}\\ y=\frac{−1}{2}x+\frac{11}{2}\end{array}$

Now, the equation is in the form $y=mx+c$. Here slope m of the line is $-\frac{1}{2}$ and intercept of y-axis c is $\frac{11}{2}$.

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 $3x-7y=-6$ and blue line denotes the equation $x+2y=11$.

Therefore, the point of intersection is $\left(5,3\right)$.

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

Substitute the point $\left(5,3\right)$in the equation $3x-7y=-6$.

Substitute x as 5 and y as $3$and check whether right hand side is equal to left hand side of the equation.

$\begin{array}{c}3\left(5\right)−7\left(3\right)=−6\\ 15−21=−6\\ −6=−6\end{array}$

Since, this is true so the point $\left(5,3\right)$satisfy the equation $3x-7y=-6$.

Substitute the point $\left(5,3\right)$ in the equation $x+2y=11$.

Substitute x as 5 and y as 3 and check whether right hand side is equal to left hand side of the equation.

$\begin{array}{c}5+2\left(3\right)=11\\ 5+6=11\\ 11=11\end{array}$

Since, this is true so the point $\left(5,3\right)$satisfy the equation $x+2y=11$.

Hence, the solution of the system of equations is $\left(5,3\right)$.