If 3|x| + 5|y| = 8 and 7|x| — 3|y| = 48, then find the value of x +

1.	If 3\|x\| + 5\|y\| = 8 and 7\|x\| — 3\|y\| = 48, then find the value of x + y. A) -5 B) 5C) -4 D) The value does not exist
Answer» Correct option is (D) The value does not exist Take \|x\| = X & \|y\| = Y Then given system of equations converts into 3X + 5Y = 8 _________(1) & 7X - 3Y = 48 _________(2) Multiply equation (1) by 3 and equation (2) by 5, we get 9X + 15Y = 24 _________(3) & 35X - 15Y = 240 _________(4) By adding equations (3) & (4), we get 44X = 264 \(\Rightarrow\) X = \(\frac{264}{44}\) = 6 \(\therefore\) \|x\| = 6 \((\because X=\|x\|)\) Put X = 6 into equation (1), we get \(3\times6+5Y=8\) \(\Rightarrow\) 5Y = 8 - 18 = -10 \(\Rightarrow\) Y = \(\frac{-10}5\) = -2 \(\therefore\) \|y\| = -2 which is not possible because mode never gives negative value. \((\because Y=\|y\|)\) Hence, value of y does not exist. Therefore, value of (x + y) does not exist. Correct option is D) The value does not exist

If 3|x| + 5|y| = 8 and 7|x| — 3|y| = 48, then find the value of x + y. A) -5 B) 5C) -4 D) The value does not exist

Answer»

Correct option is (D) The value does not exist

Take |x| = X & |y| = Y

Then given system of equations converts into

3X + 5Y = 8 _________(1)

& 7X - 3Y = 48 _________(2)

Multiply equation (1) by 3 and equation (2) by 5, we get

9X + 15Y = 24 _________(3)

& 35X - 15Y = 240 _________(4)

By adding equations (3) & (4), we get

44X = 264

\(\Rightarrow\) X = \(\frac{264}{44}\) = 6

\(\therefore\) |x| = 6 \((\because X=|x|)\)

Put X = 6 into equation (1), we get

\(3\times6+5Y=8\)

\(\Rightarrow\) 5Y = 8 - 18 = -10

\(\Rightarrow\) Y = \(\frac{-10}5\) = -2

\(\therefore\) |y| = -2 which is not possible because mode never gives negative value. \((\because Y=|y|)\)

Hence, value of y does not exist.

Therefore, value of (x + y) does not exist.

Correct option is D) The value does not exist