AP ICET 2024 6th May 2024 Shift 1

From the given equation, we have:
(‌

2

1

)x(‌

−1

1

)y=(‌

4

5

).
This simplifies to:
2x×(−1)y=‌

4

5

Since (−1)y can only be 1 or -1 , this equation only holds if y is even and 2x=‌

4

5

. Solving for x and y, we find that the equation holds when x=0 and y=0, which gives:
2x−3y=2(0)−3(0)=0.
Quick Tip
In equations involving powers, consider the properties of exponents and solve for each variable individually.