Question

Solve the following systems of equations:

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

4(y - 2) +3(x - 3)  =2

Answer 1

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

7y + 21 - 2x - 4 = 14

7y - 2x = 14 - 21 + 4

⇒ 7y – 2x = -3 ---- (1)

4(y - 2) +3(x - 3)  = 2

4y - 8 + 3x - 9 = 2

4y + 3x = 2 + 8 + 9

⇒ 4y + 3x = 19 ------ (2)

Multiplying eq1 by 3 and eq2 by 2 and adding them

3(7y – 2x) + 2(4y + 3x ) = - 3 (3) + 19(2)

⇒ 21y – 6x + 8y + 6x = - 9 + 38

⇒ 29 y = 29

⇒ y = 1

Put the value of y in (1) to get,

7 – 2x = - 3- 2x = - 3 - 7 - 2x = - 10

⇒ x = 5