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 following systems of equations:

$\frac{44}{x + y} + \frac{30}{x - y} = 10$

$\frac{55}{x + y} + \frac{40}{x - y} = 13$

Accepted Answer

The given equations are:
$\frac{44}{x + y} + \frac{30}{x - y} = 10$
$\frac{55}{x + y} + \frac{40}{x - y} = 13$
Let $\frac{1}{x + y} = u$ and $\frac{1}{x - y} = v$ , then the equations will be
$44 u + 30 v = 10 \dots (i)$
$55 u + 40 v = 13 \dots (i i)$

Multiply equation $(i)$ by $4$ and equation $(i i)$ by $3$ , subtracting equation $(i i)$ from $(i)$ , we get:
$176 u + 120 v - 165 u - 120 v = 40 - 39$
$\Rightarrow 11 u = 1$
$\Rightarrow u = \frac{1}{11}$
Putting the value of $u$ in equation $(i)$ , we get:
$44 \times \frac{1}{11} + 30 v = 10$
$\Rightarrow 30 v = 6$
$\Rightarrow v = \frac{1}{5}$
Then,
$\frac{1}{x + y} = \frac{1}{11}$
$\Rightarrow x + y = 11 \dots (i i i)$
$\frac{1}{x - y} = \frac{1}{5}$
$\Rightarrow x - y = 5 \dots (i v)$
Adding both $(i i i)$ and $(i v)$ equations, we get:
$x + y = 11$
$x - y = 5$
$2 x = 16$
$\Rightarrow x = 8$
Putting the value of $x$ in equation $(i i i)$ , we get:
$8 + y = 11$
$\Rightarrow y = 3$
Hence, the value of $x = 8$ and $y = 3$ .

Solve the following systems of equations:
$\frac{44}{x + y} + \frac{30}{x - y} = 10$

$\frac{55}{x + y} + \frac{40}{x - y} = 13$

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

Solve the following systems of equations: 44x+y+30x-y=10 55x+y+40x-y=13

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

Solve the following systems of equations:
$\frac{44}{x + y} + \frac{30}{x - y} = 10$

$\frac{55}{x + y} + \frac{40}{x - y} = 13$