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 systems of simultaneous linear equations by the multiplication method:-

$3 x + 2 y = 4$

$8 x + 5 y = 9$

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:

$3 x + 2 y = 4$

$\Rightarrow 3 x + 2 y - 4 = 0 . . . . (1)$

$8 x + 5 y = 9$

$\Rightarrow 8 x + 5 y - 9 = 0 . . . . . (2)$

Here, $a_{1} = 3, b_{1} = 2, c_{1} = - 4$

$a_{2} = 8, b_{2} = 5, c_{2} = - 9$

$\Rightarrow x = \frac{(2 \times - 9) - (5 \times - 4)}{(3 \times 5) - (8 \times 2)}; y = \frac{(- 4 \times 8) - (- 9 \times 3)}{(3 \times 5) - (8 \times 2)}$

$\Rightarrow x = \frac{- 18 + 20}{15 - 16}; y = \frac{- 32 + 27}{15 - 16}$

$\Rightarrow x = \frac{2}{- 1}; y = \frac{- 5}{- 1}$

$\Rightarrow x = - 2; y = 5$

M L Aggarwal Solutions for Exercise 3: EXERCISE 5.3

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 3: EXERCISE 5.3

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