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

Q3.    Solve the following pair of linear equations by the substitution and cross-multiplication methods :
                \\8x + 5y = 9 \\3x + 2y = 4

Answers (2)

best_answer

Given the equations 

\\8x + 5y = 9........(1) \\3x + 2y = 4........(2)

By Substitution Method,

From (1) we have 

y=\frac{9-8x}{5}.........(3)

Substituting this in (2), 

3x+2\left ( \frac{9-8x}{5} \right )=4

\Rightarrow 15x+18-16x=20

\Rightarrow -x=20-18

\Rightarrow x=-2

Substituting this in (3)

y=\frac{9-8x}{5}=\frac{9-8(-2)}{5}=\frac{25}{5}=5

Hence x=-2\:and\:y=5.

By Cross Multiplication Method

\frac{x}{b_1c_2-b_2c_1}=\frac{y}{c_1a_2-c_2a_1}=\frac{1}{a_1b_2-a_2b_1}

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

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

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

x=-2,\:and\:y=5

Posted by

Pankaj Sanodiya

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X=-2

y=5

Posted by

Manu

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