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

Show graphically that each one of the following systems of equations is inconsistent (i.e. has no solution) :

$3 x - 5 y = 20$
$6 x - 10 y = - 4$

Accepted Answer

The given equations are:
$3 x - 5 y = 20$ . $6 x - 10 y = - 4$
$6 x - 10 y = - 4$ ….. $(i i)$

Putting $x = 0$ in equation $(i)$ we get:
$\Rightarrow 3 \times 0 - 5 y = 20$
$\Rightarrow y = - 4$
$x = 0, y = - 4$
Putting $y = 0$ in equation $(i)$ we get:
$\Rightarrow 3 x - 5 \times 0 = 20$
$\Rightarrow x = \frac{20}{3}$
$x = \frac{20}{3}, y = 0$
Use the following table to draw the graph.

$x$ $0$ $\frac{20}{3}$

$y$ $- 4$ $0$

Draw the graph by plotting the two points $A (0, - 4)$ and $B (\frac{20}{3}, 0)$ from table.

Graph of the equation $(i i)$ :
$6 x - 10 y = - 4 . . . . (i i)$

Putting $x = 0$ in equation $(i i)$ we get:
$\Rightarrow 6 \times 0 - 10 y = - 4$
$\Rightarrow y = \frac{2}{5}$
$y = \frac{2}{5}, x = 0$
Putting $y = 0$ in equation $(i i)$ we get:
$\Rightarrow 6 x - 10 \times 0 = - 4$
$\Rightarrow x = - \frac{2}{3}$
$x = - \frac{2}{3}, y = 0$
Use the following table to draw the graph.

$x$ $0$ $- \frac{2}{3}$

$y$ $\frac{2}{5}$ $0$

Draw the graph by plotting the two points $C (0, - \frac{2}{5})$ and $D (- \frac{2}{3}, 0)$ from table:

Here the graph of the two equations are parallel to each other.
Hence, the pair of linear equations having no solution is inconsistent.

Show graphically that each one of the following systems of equations is inconsistent (i.e. has no solution) :

$3 x - 5 y = 20$
$6 x - 10 y = - 4$

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

Show graphically that each one of the following systems of equations is inconsistent (i.e. has no solution) : 3x-5y=20 6x-10y=-4

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

Show graphically that each one of the following systems of equations is inconsistent (i.e. has no solution) :

$3 x - 5 y = 20$
$6 x - 10 y = - 4$