If [ 2 x + y 4 x 5 x − 7 4 x ] = [ 7 7 y − 13 y x + 6 ] , then x + y =

Explanation: As we know,When two matrices are equal, all the corresponding elements must be equal.Given, [ 2 x + y 4 x 5 x − 7 4 x ] = [ 7 7 y − 13 y x + 6 ] Comparing two elements of first column, 2 x + y = 7 ⇒ y = 7 − 2 x ...(1) 5 x − 7 = y ...(2)Compairing value of y from equation (1) and (2) we get, 7 − 2 x = 5 x − 7 ⇒ 7 + 7 = 5 x + 2 x ⇒ 14 = 7 x ∴ x = 2 Putting value of x in equation (1), we get y = 7 − 2 × 2 ⇒ y = 7 − 4 ⇒ y = 3 Now, x + y = 2 + 3 = 5 So, the value of x + y is 5 .Hence, the correct option is (C).

Question:

If $[\begin{array}{cc} 2 x + y & 4 x \\ 5 x - 7 & 4 x \end{array}] = [\begin{array}{cc} 7 & 7 y - 13 \\ y & x + 6 \end{array}]$ , then $x + y =$

MHT CET

Updated On: May 4, 2024

(A) 3
(B) 4
(C) 5
(D) 6

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The Correct Option is C

Solution and Explanation

Explanation:
As we know,When two matrices are equal, all the corresponding elements must be equal.Given,

[\begin{array}{cc} 2 x + y & 4 x \\ 5 x - 7 & 4 x \end{array}] = [\begin{array}{cc} 7 & 7 y - 13 \\ y & x + 6 \end{array}]

Comparing two elements of first column,

2 x + y = 7

\Rightarrow y = 7 - 2 x

...(1)

5 x - 7 = y

...(2)Compairing value of

y

from equation (1) and (2) we get,

7 - 2 x = 5 x - 7

\Rightarrow 7 + 7 = 5 x + 2 x

\Rightarrow 14 = 7 x

∴ x = 2

Putting value of

x

in equation (1), we get

y = 7 - 2 \times 2

\Rightarrow y = 7 - 4

\Rightarrow y = 3

Now,

x + y = 2 + 3 = 5

So, the value of

x + y

5

.Hence, the correct option is (C).

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Questions Asked in MHT CET exam

If $[\begin{array}{cc} 2 x + y & 4 x \\ 5 x - 7 & 4 x \end{array}] = [\begin{array}{cc} 7 & 7 y - 13 \\ y & x + 6 \end{array}]$ , then $x + y =$