Question

On the same axes, draw the graph of each of the following equations: $2y-x=8,5y-x=14,y-2x=1$. Hence, obtain the vertices of the triangle so formed.

• A. $(1,2),(-1,2),(1,6)$
• B. $(2,5),(-4,2),(1,3)$
• C. $(-2,2),(5,-7),(2,9)$
• D. $(1,-3),(2,-3),(2,-7)$

Answer 1

Answer: (B)

$(2,5),(-4,2),(1,3)$

$2y-x=8$

$⟹x=2y-8$

Let, $y=2$, then $x=2\left(2\right)-8=-4$,

$y-2x=1$

$⟹y=1+2x$

Let, $x=1$, then $y=1+2\left(1\right)=3$

Similarly, when $x=2,y=5$

and $5y-x=14$

$⟹x=5y-14$

let, $y=3$then $x=5\left(3\right)-14=1$

Similarly, when, $y=2,x=-4$

Plotting the above points on the graph, we get intersection points

$A(-4,2),B(2,5),C(1,3)$