For the equations ax + (a2 + 1)y = 4 and 4x + ay = a2, which of the following statements is TRUE?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. If a = −12 then x = 48, Y = 4 are the solutions.
ax + (a2 + 1)y = 4 .....(1)
If a = -12 and y = 4 then we get from equation (1),
(-12)x + [(-12)2 + 1]4 = 4
⇒ -12x + (145 × 4) = 4
⇒ - 12x + 580 = 4
⇒ -12x = 4 - 580 = -576
⇒ x = -576/-12 = 48
Also, 4x + ay = 4 × 48 + (-12) × 4 = 144 = a2
Hence, it is the solution.