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:
$2 x - 5 y + 4 = 0 2 x + y - 8 = 0$

Find the vertices and area of the triangle formed by these lines and the $y$ -axis.

Accepted Answer

On a graph paper, draw a horizontal line $2 x - 5 y + 4 = 0 2 x + y - 8 = 0$ and a vertical line $y o y$ as the $x$ -axis and $y$ -axis respectively.
Graph of:

$2 x - 5 y + 4 = 0$

$5 y = (2 x + 4)$

$y = \frac{(2 x + 4)}{5} . . . . . . . (i)$
Putting $x = - 2$ , we get $y = 0$ .
Putting $x = 3$ , we get $y = 2$ .
Putting $x = 8$ , we get $y = 4$ .
Thus, we have the following table for the equation $2 x - 5 y + 4 = 0$ .

$x$ $- 2$ $3$ $8$

$y$ $0$ $2$ $4$

Now, plot the points $A (- 2, 0), B (3, 2)$ and $C (8, 4)$ on the graph paper.
Join $A B$ and $B C$ to get the graph line $A C$ . Extend it on both ways.
Thus, $A C$ is the graph of $2 x - 5 y + 4 = 0$ .

Graph of $2 x + y - 8 = 0$
$2 x + y - 8 = 0$

$y = (8 - 2 x) . . . . . . . . (i i)$
Putting $x = 1$ , we get $y = 6$ .
Putting $x = 3$ , we get $y = 2$ .
Putting $x = 2$ , we get $y = 4$ .
Thus, we have the following table for the equation $2 x + y - 8 = 0$ .

$x$ $1$ $3$ $2$

$y$ $6$ $2$ $4$

Now, plot the points $P (1, 6)$ and $Q (2, 4)$ . The point $B (3, 2)$ has already been plotted. Join $P Q$ and $Q B$ and extend it on both ways.
Thus, $P B$ is the graph of $2 x + y - 8 = 0$ .

The two graph lines intersect at $B (3, 2)$ .
$∴ x = 3$ and $y = 2$ .

Now, area of the triangle $= \frac{1}{2} (b a s e \times h e i g h t)$

Hence, Area $= \frac{1}{2} (7 \times 3) = \frac{21}{2} = 10.5 sq$ . units

Solve the system of equations graphically:
$2 x - 5 y + 4 = 0 2 x + y - 8 = 0$

Find the vertices and area of the triangle formed by these lines and the $y$ -axis.

Important Questions on Linear Equations in Two Variables

Learn and Prepare for any exam you want !

Solve the system of equations graphically: 2x-5y+4=02x+y-8=0 Find the vertices and area of the triangle formed by these lines and the y-axis.

Important Questions on Linear Equations in Two Variables

Learn and Prepare for any exam you want !

Solve the system of equations graphically:
$2 x - 5 y + 4 = 0 2 x + y - 8 = 0$

Find the vertices and area of the triangle formed by these lines and the $y$ -axis.