Question

Solve the following systems of equations:
$\frac{x}{3} +\frac{y}{4}=11$
$\frac{5x}{6} -\frac{y}{3}= -7$

Answer 1

Given, pair of linear equations:  

x/3 + y/4 = 11 ………..(1)

5x/6 - y/3 = - 7 …………(2)

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

This equations can be written as :  

From eq 1 :

(4x + 3y)/12 = 11

4x + 3y = 11 × 12

4x + 3y = 132 ………(3)

From eq 2 :  

(5x - 2y)/6  = - 7

5x - 2y = -7  × 6

5x - 2y = - 42 ………(4)

From eq (3) :  

4x = 132 - 3y  

x = (132 - 3y)/4 ………..(5)

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

5x - 2y = - 42

5(132 - 3y)/4 - 2y = - 42

(660 - 15y)/4  - 2y = - 42

660 - 15y - 8y = - 42 × 4

660 - 23y  = - 168

-23y = - 168 - 660

- 23y = - 828

y = 828/23

y = 36

On putting y = 36 in eq (5)  we get,

x = (132 - 3y)/4

x = (132 - 3 × 36)/4

x = (132 - 108)/4

x = 24/4

x = 6

Hence the solution of the given system of equation is x = 6 and y = 36.

Hope this answer will help you…

 

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Answer 2

multiplying by 12, then

4x+3y =132.......(1)

5x/6-y/3+7 =0

5x/6-y/3= -7

multiplying by 18, then

15x-6y= -126........(2)

in equation (1) multiplying by 2, then, 8x+6y =264........(3)

(2)+(3)

we get, 23x =138

ie, x= 138/23= 6

ie, x=6

put the value of x into equation (1), we get,

24+3y=132

3y =108

y =36

we get the values are x=6 and

y = 36