Solve the following equations by the substitution method 129x-10y-23- 5x4-2y-3

The correct option is A x = 4, y =1 The equations are ⇒1/2 ( 9x+10y )=23⇒ 9x+10y=46....eq ( 1 ) ⇒ #160; x=46 10y/9 ⇒5x/4 2y=3⇒ 5x 8y=12. ...

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Standard X

Mathematics

Method of Substitution to Find the Solution of a Pair of Linear Equations

Solve the fol...

Question

Solve the following equations by the substitution method
$\frac{1}{2} (9 x + 10 y) = 23, \frac{5 x}{4} - 2 y = 3$

x = 4, y = 1

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x = 2, y = 5

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x = 1, y = - 1

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x = 7, y = - 3

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Solution

The correct option is A $x = 4, y = 1$
The equations are
$\Rightarrow \frac{1}{2} (9 x + 10 y) = 23 \Rightarrow 9 x + 10 y = 46.... e q (1)$
$\Rightarrow x = \frac{46 - 10 y}{9}$
$\Rightarrow \frac{5 x}{4} - 2 y = 3 \Rightarrow 5 x - 8 y = 12.... e q (2)$
Substitute the value of x in eq (2 )
$\Rightarrow \frac{5 (46 - 10 y)}{9} - 8 y = 12$
$\Rightarrow 230 - 50 y - 72 y = 108 \Rightarrow - 122 y = - 122 \Rightarrow y = 1$
Substitute the value of y in eq (2 )
$\Rightarrow 5 x - 8 (1) = 12 \Rightarrow 5 x = 20 \Rightarrow x = 4$
$\Rightarrow x = 4, y = 1$

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Solve the following equations by the substitution method12(9x+10y)=23,5x4−2y=3

Solve the following equations by the substitution method
$\frac{1}{2} (9 x + 10 y) = 23, \frac{5 x}{4} - 2 y = 3$