SSC CGL 2024 PYQ — Question 62

The correct answer is  option 3  i.e. x =5, y = 3, z = 8.

5x - 3y + 7z = 22      (1)

3x - 5y - 2z = -46      (2)

 2x - 2y + 5z = 24       (3)

 Equation (3) to express (x) in terms of (y) and (z). 

⇒ 2x - 2y + 5z = 24

⇒ 2x = 2y - 5z + 24

⇒ x = y -  5 / 2z + 12

(x = y - 5/ 2z + 12), substitute this into Equations (1) and (2).

⇒$5\left(y - \frac{5}{2}z + 12\right) - 3y + 7z = 22$

⇒ 5y - 25 / 2z + 60 - 3y + 7z = 22

⇒ $(5y - 3y) + \left(- \frac{25}{2}z + 7z\right) = 22 - 60$

⇒ $2y + \left( - \frac{25}{2}z + \frac{14}{2}z\right) = -38$

⇒ 2y - 11 / 2z = -38

⇒ 4y - 11z = -76     ( 4)

(x = y - 5 / 2z + 12\) into Equation (2):

⇒ $3\left(y - \frac{5}{2}z + 12\right) - 5y - 2z = -46$

⇒ $3y - \frac{15}{2}z + 36 - 5y - 2z = -46$

⇒ $(3y - 5y) + \left( - \frac{15}{2}z - 2z \right) = -46 - 36$

⇒$-2y - \left( \frac{15}{2}z + \frac{4}{2}z \right) = -82$

⇒ $-2y - \frac{19}{2}z = -82$

⇒ -4y - 19z = -164   (5)

1. (4y - 11z = -76) (Equation 4)

2. (-4y - 19z = -164) (Equation 5)

Add these equations to eliminate (y):

⇒ (4y - 11z) + (-4y - 19z) = -76 + (-164)

⇒ -30z = -240

⇒z = 8

z = 8  into Equation (4):

⇒ 4y - 11(8) = -76

⇒ 4y - 88 = -76

⇒ 4y = 12

⇒ y = 3

⇒$x = 3 - \frac{5}{2}(8) + 12$

⇒ x = 3 - 20 + 12

⇒ x = -5

x =  -5,  y = 3,  z = 8