2y-x=8,5y-x =14,-x+y/2=1/2 are vertices of triangle. …

{tex}2y - x = 8{/tex}
{tex}5y - x = 14{/tex}
{tex}y - 2x = 1{/tex}
Now, {tex}2y - x = 8{/tex}
{tex}x = 2y - 8{/tex}
When {tex}y = 2{/tex} then {tex}x = - 4{/tex}
When {tex}y = 5{/tex} then {tex}x = 2{/tex}
Thus, we have the following table giving points on the line {tex}2y - x = 8{/tex}

Now, {tex}5y - x = 14{/tex}
{tex}x = 5y - 14{/tex}
When {tex}y = 2{/tex}, then {tex}x = 1{/tex}
When {tex}y = 3{/tex} , then {tex}x = 1{/tex}
Thus, we have the following table giving points on the line {tex}5y - x = 14{/tex}

We have,
{tex}y - 2x = 1{/tex}
{tex}x = \frac{{y - 1}}{2}{/tex}
When {tex}y = -1{/tex}, then {tex}x = 1{/tex}
When {tex} y = 3{/tex} , then {tex}x = 1{/tex}
Thus, we have the following table giving points on the line {tex}y - 2x = 1{/tex}

From the graph of the lines represent by the given equation, we observe that the lines taken in pairs intersect at points A(-4, 2) B(1, 3) and C(2, 5).
Hence the vertices of the triangle are A(-4, 2) B(1, 3) and C(2, 5)