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AP ICET 2024 6th May 2024 Shift 1

Question : 154 of 200

Marks: +1, -0

{\begin{array}{rr} 2 & -1 \\ 1 & 1 \end{array}}\binom{x}{y}=\binom{4}{5}

2 x-3 y=

Solution:

From the given equation, we have:

\left(\frac{2}{1}\right)^x \left(\frac{-1}{1}\right)^y = \left(\frac{4}{5}\right) .

This simplifies to:

2^x \times (-1)^y = \frac{4}{5}

Since

(-1)^y

can only be 1 or -1 , this equation only holds if

y

is even and

2^x = \frac{4}{5}

. Solving for

x

and

y

, we find that the equation holds when

x=0

and

y=0

, which gives:

2 x-3 y=2(0)-3(0)=0 .

Quick Tip

In equations involving powers, consider the properties of exponents and solve for each variable individually.

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