Name: Equations Reducible to a Pair of Linear Equations
Uploaded: 2019-07-19
Duration: 4 min 9 s
Description: Some equations may be in a form that can be reduced to a linear equation through substitution. Do you want to explore how this can be done? Watch the video t...

Question

Solve the following pairs of linear equations by cross- multiplication method:

$2 b x + a y = 2 a b$

$b x - a y = 4 a b$

Accepted Answer

The solution of system of simultaneous linear equation is given as

$\frac{x}{b_{1} c_{2} - b_{2} c_{1}} = \frac{y}{c_{1} a_{2} - c_{2} a_{1}} = \frac{1}{a_{1} b_{2} - a_{2} b_{1}}$

$\Rightarrow x = \frac{b_{1} c_{2} - b_{2} c_{1}}{a_{1} b_{2} - a_{2} b_{1}}; y = \frac{c_{1} a_{2} - c_{2} a_{1}}{a_{1} b_{2} - a_{2} b_{1}}$

The given equations are:

$2 b x + a y = 2 a b$

$\Rightarrow 2 b x + a y - 2 a b = 0 . . . . (1)$

$b x - a y = 4 a b$

$\Rightarrow b x - a y - 4 a b = 0 . . . . . (2)$

Here, $a_{1} = 2 b, b_{1} = a, c_{1} = - 2 a b$

$a_{2} = b, b_{2} = - a, c_{2} = - 4 a b$

$\Rightarrow x = \frac{(a \times - 4 a b) - (- a \times - 2 a b)}{(2 b \times - a) - (b \times a)}; y = \frac{(- 2 a b \times b) - (- 4 a b \times 2 b)}{(2 b \times - a) - (b \times a)}$

$\Rightarrow x = \frac{- 4 a^{2} b - 2 a^{2} b}{- 2 a b - a b}; y = \frac{- 2 a b^{2} + 8 a b^{2}}{- 2 a b - a b}$

$\Rightarrow x = \frac{- 6 a^{2} b}{- 3 a b}; y = \frac{6 a b^{2}}{- 3 a b}$

$\Rightarrow x = 2 a; y = - 2 b$

Solve the following pairs of linear equations by cross- multiplication method:

$2 b x + a y = 2 a b$

$b x - a y = 4 a b$

Important Questions on Simultaneous Linear Equations

Learn and Prepare for any exam you want !

Solve the following pairs of linear equations by cross- multiplication method: 2bx+ay=2ab bx-ay=4ab

Important Questions on Simultaneous Linear Equations

Learn and Prepare for any exam you want !

Solve the following pairs of linear equations by cross- multiplication method:

$2 b x + a y = 2 a b$

$b x - a y = 4 a b$