Name: Cross Multiplication Method: Illustration
Uploaded: 2019-07-19
Duration: 7 min 27 s
Description: This tutorial will show you many examples of solving linear equations in two variables using the cross-multiplication method with a clear step-by-step explan...

Question

Solve the system of equations graphically:
$2 x + 3 y = 8$

$x - 2 y + 3 = 0$

Accepted Answer

On a graph paper, draw a horizontal line $2 x + 3 y = 8$ and a vertical line $Y O Y'$ as the $x$ -axis and $y$ -axis, respectively.
Graph of $2 x + 3 y = 8$ .
$2 x + 3 y = 8$

$3 y = (8 - 2 x)$

$y = \frac{(8 - 2 x)}{3} . . . . \dots (i)$
Putting $x = 1$ , we get $y = 2$ .
Putting $x = - 5$ , we get $y = 6$ .
Putting $x = 7$ , we get $y = - 2$ .
Thus, we have the following table for the equation $2 x + 3 y = 8$ .

$x$ $1$ $- 5$ $7$

$y$ $2$ $6$ $- 2$

Now, plot the points $A (1, 2), B (5, - 6)$ and $C (7, - 2)$ on the graph paper.
Join $A B$ and $A C$ to get the graph line $B C$ . Extend it on both ways.
Thus, $B C$ is the graph of $2 x + 3 y = 8$ .

Graph of $x - 2 y + 3 = 0$
$x - 2 y + 3 = 0$

$2 y = (x + 3)$

$y = \frac{(x + 3)}{2} . . . . . . . (i i)$
Putting $x = 1$ , we get $y = 2$ .
Putting $x = 3$ , we get $y = 3$ .
Putting $x = - 3$ , we get $y = 0$ .
Thus, we have the following table for the equation $x - 2 y + 3 = 0$ .

$x$ $1$ $3$ $- 3$

$y$ $2$ $3$ $0$

Now, plot the points $P (3, 3)$ and $Q (- 3, 0)$ . The point $A (1, 2)$ has already been plotted. Join $A P$ and $Q A$ and extend it on both ways.
Thus, $P Q$ is the graph of $x - 2 y + 3 = 0$ .

The two graph lines intersect at $A (1, 2)$ .
$∴ x = 1$ and $y = 2$ .

Solve the system of equations graphically:
$2 x + 3 y = 8$

$x - 2 y + 3 = 0$

Important Questions on Linear Equations in Two Variables

Learn and Prepare for any exam you want !

Solve the system of equations graphically: 2x+3y=8 x–2y+3=0

Important Questions on Linear Equations in Two Variables

Learn and Prepare for any exam you want !

Solve the system of equations graphically:
$2 x + 3 y = 8$

$x - 2 y + 3 = 0$