Find the value of the unknowns:
x + 1.5y + 2z = 5.5
x + 5y + 7z = 15
3x + 11y + 13z = 25
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. x = 2,y = -3,z = 4.
x + 1.5y + 2z = 5.5 .....(1)
x + 5y + 7z = 15 .....(2)
3x + 11y + 13z = 25 .....(3)
Subtract the equation (1) from equation (2),
3.5y + 5z = 9.5 .....(4)
Multiply the equation (1) by 3 and subtract it from third equation (3),
(3x + 11y + 13z) - 3(x + 1.5y + 2z) = 25 - 3(5.5)
⇒ 6.5y + 7z = 8.5 .....(5)
Multiply equation (4) by 6.5 and second (5) by 3.5, then subtract equation (6) from (5),
6.5(3.5y + 5z) - 3.5(6.5y + 7z) = (9.5 × 6.5) - (8.5 × 3.5)
⇒ 22.75y + 32.5z - 22.75y - 24.5z = 61.75 - 29.75
⇒ 8z = 32
⇒ z = 32/8 = 4
Putting z = 4 into the equation (5),
3.5y + 5(4) = 9.5
⇒ 3.5y = -10.5
⇒ y = -3
Putting y = -3 and z = 4 into the equation (1),
x + 1.5(-3) + 2(4) = 5.5
⇒ x - 4.5 + 8 = 5.5
⇒ x = 2
Therefore, x = 2, y = -3, and z = 4.