Solve the following pair of linear equations by the substitution and cross-multiplication methods:
$8x + 5y = 9$
$3x + 2y = 4$

Given:

$8x + 5y = 9$

$3x + 2y = 4$

To do:

We have to solve the given pair of linear equations by the substitution and cross-multiplication methods.

Solution:

By substitution method:

$8x+5y=9$

This implies,

$x=\frac{9-5y}{8}$.....(i)

$3x+2y=4$

$3(\frac{9-5y}{8})+2y=4$            [From (i)]

$\frac{27-15y}{8}=4-2y$

$27-15y=8(4-2y)$

$27-15y=32-16y$

$16y-15y=32-27$

$y=5$

Therefore,

$x=\frac{9-5(5)}{8}$

$x=\frac{9-25}{8}$

$x=\frac{-16}{8}$

$x=-2$

 By cross multiplication method,we get,

$\frac{x}{5(4)-(2)(9)}=\frac{y}{9(3)-(4)(8)}=\frac{-1}{8(2)-3(5)}$

$\frac{x}{20-18}=\frac{y}{27-32}=\frac{-1}{16-15}$

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

$x=-1(2)$ and $y=-1(-5)$

$x=-2$ and $y=5$

The values of $x$ and $y$ are $-2$ and $5$ respectively.

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Updated on: 10-Oct-2022

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