Question

If 3x+2|y|+y=7 and x+|x|+3y=1, then x+2y is

• A. 0
• B. 1
• C. $\frac{-4}{3}$
• D. $\frac{8}{3}$

Answer 1

Answer: (A)

0

Answer 2

Let's solve for x and y using the given equations:

Given:
1)$3x + 2|y| + y = 7$
2) $x + |x| + 3y = 1$

From the second equation:
$x + |x| = 1 - 3y$

Case 1: x ≥ 0 In this case,$|x| = x$, so: $x + x = 1 - 3y$ $2x = 1 - 3y$ $x = 0.5 - 1.5y$... (i)
Case 2: x < 0 In this case, $|x| = -x$, so: $x - x = 1 - 3y$

This gives us 0 = 1 - 3y, which is not possible.

Hence, the first case is our valid scenario.

Substitute the value of x from equation (i) into the first equation:
$3(0.5 - 1.5y) + 2|y| + y = 7$

Expanding:
$1.5 - 4.5y + 2|y| + y = 7$
$1.5 - 3.5y + 2|y| = 7$
$-3.5y + 2|y| = 5.5$

Now, for y:

Case 1 : y ≥ 0

In this case, $|y| = y$:
$-3.5y + 2y = 5.5$
$-1.5y = 5.5$

This gives a negative value for y, which is not possible in this case.

Case 2 : y < 0 In this case,
$|y| = -y$: $-3.5y - 2y = 5.5$
$-5.5y = 5.5$
$y = -1$

Substituting this value of y in equation (i):
$x = 0.5 - 1.5(-1)$
$x = 0.5 + 1.5 = 2$

So,$x = 2$ and $y = -1$.

Finally, $x + 2y = 2 + 2(-1) = 2 - 2 = 0$