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.

The intersection points of the equations represent the vertices of the triangle.

Consider the equations.

$y-2x=1,4x+y=7,\text{and}2y-x=-4$

Consider the first equation$y-2x=1$.

Rewrite the equation in form of slope-intercept form.

Add both sides $2x$

$\begin{array}{l}y−2x+2x=1+2x\\ y=1+2x\\ y=2x+1\end{array}$

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 $1$.

Now, consider the second equation$4x+y=7$.

Rewrite the equation in form of slope-intercept form.

Subtract both sides by $4x$

$\begin{array}{l}4x+y−4x=7−4x\\ y=7−4x\\ y=−4x+7\end{array}$

Now, the equation is in the form$y=mx+c$. Here slope m of the line is $-4$ and intercept of y-axis c is 7.

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

Rewrite the equation in form of slope-intercept form.

Add both sides$x$

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

Divide both sides by 2.

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

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 $-2$

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 $y-2x=1$, blue line denotes the equation$4x+y=7$and green line denotes the equation $2y-x=-4$.

Therefore, the point of intersections are $\left(1,3\right),\left(-2,-3\right),\left(2,-1\right)$.

Thus, the coordinates of vertices of the triangle are$\left(1,3\right),\left(-2,-3\right),\left(2,-1\right)$.