Question

Solve the following systems of equations:
$\frac{x}{7} +\frac{y}{3}=5$
$\frac{x}{2} -\frac{y}{9}=6$

Answer 1

Given, pair of linear equations:  

x/7 + y/3 = 5 ………..(1)

x/2 - y/9 = 6 …………(2)

Substitution method is used to solve this Linear pair of Equations.

This equations can be written as :  

From eq 1 :

(3x + 7y)/21 = 5

3x + 7y = 5 × 21

3x + 7y = 105 ………(3)

From eq 2 :  

(9x - 2y)/18 = 6

9x - 2y = 6 × 18

9x - 2y = 108 ………(4)

From eq (3) :  

3x = 105 - 7y  

x = (105 - 7y)/3 ………..(4)

On Substituting the value of x in equation (4) we obtain :  

9x - 2y = 108

9(105 - 7y)/3 - 2y = 108

(945 - 63y)/3  - 2y = 108

945 - 63y - 6y = 108 × 3

945 - 63y - 6y = 324

-69y = 324 - 945

69y = 621

y = 621/69

y = 9

On putting y = 9 in eq (4)  we get,

x = (105 - 7 × 9)/3

x = (105 - 63)/3

x = 42/3

x = 14

Hence the solution of the given system of equation is x = 14 and y = 9.

Hope this answer will help you…

 

Some more similar questions from this chapter :  

Solve the following systems of equations:

x/2 + y = 0.8  

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Solve the following systems of equations:

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Answer 2

AnswEr :

$\underline{\bigstar\:\textsf{By \: Sublimation \; method:}}$

⋆ $\sf\ Equation \: 1 : \: \frac{x}{7} + \frac{y}{3} = 5$

$\sf\longrightarrow\frac{x}{7} + \frac{y}{3} = 5 \\\\\\\sf\longrightarrow\frac{3x + 7y }{21} = 5 \\\\\\\sf\longrightarrow\ 3x + 7y = 105 \\\\\\\sf\longrightarrow\ 3x = 105 - 7y \\\\\\\sf\longrightarrow\ x = \frac{105 - 7y}{3} \: \: \: \qquad\sf\ - (3)$

$\rule{170}{2}$

⋆ $\sf\ Equation \: 2 : \: \frac{x}{2} - \frac{y}{9} = 6$

$\sf\longrightarrow\frac{x}{2} - \frac{y}{9} = 6 \\\\\\\sf\longrightarrow\frac{9x - 2y}{18} = 6 \\\\\\\sf\longrightarrow\ 9x - 2y = 108 \\\\\\\scriptsize\qquad\dag\sf\ putting \: the \: value \: of \: x \: from \: (3) \\\\\\\sf\longrightarrow\ 9\big[\frac{105 - 7y}{3} \big] - 2y = 108 \\\\\\\sf\longrightarrow\big[\frac{945 - 63y}{3} \big] - 2y = 108\\\\\\\sf\longrightarrow\ 945 - 63y - 6y = 324\\\\\\\sf\longrightarrow\ 945 - 69y = 324 \\\\\\\sf\longrightarrow\ -69y = 324 - 945 \\\\\\\sf\longrightarrow\ -69y = -621 \\\\\\\sf\longrightarrow\ y = \frac{\cancel{-621}}{\cancel{-69}} \\\\\\\longrightarrow\boxed{\bf\ y = 9}$

$\underline{\bigstar\:\textsf{Putting \: the \: value \: of \: y :}}$

$\sf\longrightarrow\ x = \frac{105 - 7y}{3} \\\\\\\sf\longrightarrow\ x = \frac{105 - 7(9)}{3} \\\\\\\sf\longrightarrow\ x = \frac{105 - 63}{3} \\\\\\\sf\longrightarrow\ x = \frac{42}{3} \\\\\\\sf\longrightarrow\ x = \frac{\cancel{42}}{\cancel{3}} \\\\\\\longrightarrow\boxed{\bf\ x = 14}$