Question

if |3x+y|+|y-z|=0 and x=-7, what is the value of z

Answer 1

Answer:

21

Step-by-step explanation:

The equation that we have to solve for z is:

$|3x+y|+|y-z|=0$

Here we also know that

x = -7

Substituting into the equation, we get:

$|3\cdot (-7)+y|+|y-z|=0\\|-21+y|+|y-z|=0$

By looking at the equation, we observe that here we have the sum of two terms which are absolute values; since an absolute value is always equal or greater than zero, this means that the sum of the two terms must be also equal or greater than zero.

However, we see that the equation has a sign = 0: this means that the sum of the two terms must be = 0. But this means that each of the two terms must be equal to zero (because none of them can be negative), so we have:

$-21+y=0\\y-z=0$

From eq.(1) we get

$y=21$

And so from eq.(2) we get

$z=y=21$