Question

Determine, graphically, the vertices of the triangle formed by the lines $y=x,3y=x,x+y=8$

Answer 1

Given: linear equations are

$$\begin{gathered} y=x\dots \left(i\right) \\ 3y=x\dots \left(ii\right) \end{gathered}$$

and $x+y=8\dots \left(iii\right)$

Table for line$y=x$ is tabulated below,

By substituting value of $x$ as $0,1and2$ one by one we will get $y$ as$0,1and2$

$x$	$0$	$1$	$2$
$y$	$0$	$1$	$2$

Table for line $x=3y$ is tabulated below,,

By substituting value of $y$ as $0,1and2$ one by one we will get $x$ as$0,3and6$

$x$	$0$	$3$	$6$
$y$	$0$	$1$	$2$

Table for line $x+y=8$ is tabulated below,

By substituting value of $x$ as $0,4and8$ one by one we will get $y$ as$8,4and0$

$x$	$0$	$4$	$8$
$y$	$8$	$4$	$0$

On plotting the points $A(1,1),B(2,2),C(3,1),D(6,2)$, we get the straight lines$ABandCD$.

Plotting the point$P(0,8),Q(4,4)andR(8,0)$, we get the straight line$PQR$.

$ABandCD$ intersect the line$PRonQandD$, respectively.

So, $△OQD$ is formed by these lines.

Hence, the vertices of the$△OQD$ formed by the given lines are $O(0,0),Q(4,4)andD(6,2).$