Question

Solve the following systems of equations:
7(y + 3) - 2(x + 2) = 14
4(y - 2) + 3(x - 3) = 2

Answer 1

Given, pair of linear equations:  

7(y + 3) - 2(x + 2) = 14 …………..(1)

4(y - 2) + 3(x - 3) = 2 …………(2)

The given system of equation can be written as :  

From eq (1) :  

7y + 21 - 2x - 4 = 14

7y = 14 + 4 - 21 + 2x

7y = 18 - 21 + 2x

7y = 2x - 3

y = (2x - 3)/7…………(3)

 

From eq (2) :  

4y - 8 + 3x - 9 = 2

4y + 3x - 17 - 2 = 0

4y + 3x - 19 = 0 …........(4)

On Substituting the value of y from eq 3 in equation (4) :  

4(2x - 3)/7 + 3x - 19 = 0

(8x - 12)/7 + 3x = 19

(8x - 12 + 7 × 3x)/7 = 19

(8x - 12 + 21x) = 19 × 7

29x - 12 = 133

29x = 133 + 12

29x = 145

x = 145/29

x = 5

On putting x = 5 in eq (3)  we get,

y = (2x - 3)/7

y = (2 × 5 - 3)/7

y = (10 - 3)/7

y = 7/7

y = 1

Hence the solution of the given system of equation is x = 5 and y = 1

Hope this answer will help you…

 

Some more similar questions from this chapter :  

Solve the following systems of equations:

x/2 + y = 0.8  

7/(x + y/2) = 10

https://brainly.in/question/17117800

 

Solve the following systems of equations:

0.4x + 0.3y = 1.7

0.7x - 0.2y = 0.8

https://brainly.in/question/17116587

Answer 2

Question:

Solve the following systems of equations:

7(y + 3) - 2(x + 2) = 14

4(y - 2) + 3(x - 3) = 2

Answer:

Simplifying this eq.n

$\large{ \sf{ \to \: 7y + 21 - 2x - 4 = 14}} \\ \large{ \sf{ \to \: 7y - 2x + 17 = 14}} \\ \large{ \sf{ \to \: 7y - 2x = - 3}}.....(1)$

$\large{ \sf{ \to \: 4y - 8 + 3x - 9 = 2}} \\ \large{ \sf{ \to \: 4y + 3x - 17 = 2}} \\ \large{ \sf{ \to \: 4y + 3x = 19}}....(2)$

By substitution method...

$\large{ \sf{ \implies{7y = 2x - 3}}} \\ \large{ \sf{ \implies{y = \frac{2x - 3}{7} }}}$

Putting value of y in Eq.(2)

$\large{ \sf{ \to \: 4 \times \frac{2x - 3}{7} + 3x = 19}} \\ \large{ \sf{ \to \: \frac{8x - 12}{7} + 3x = 19}} \\ \large{ \sf{ \to \: \frac{8x - 12 + 21x}{7} = 19}} \\ \large{ \sf{ \to \: \frac{29x - 12}{7} = 19}} \\ \large{ \sf{ \to \: 29x - 12 = 133}} \\ \large{ \sf{ \to \: 29x = 145}} \\ \large{ \sf{ \rightarrow{ \boxed{x = 5}}}}$

Putting the value of x in Equation (1)

$\large{ \sf{ \implies{y = \frac{2(5) - 3}{7} }}} \\ \large{ \sf{ \implies{y = \frac{7}{7} }}} \\ \large{ \sf{ \implies{ \boxed{y = 1}}}}$

So final answer:

$\huge{ \boxed{ \bold{ \red{x = 5 \: \: \: \: y = 1}}}}$