Question

$3x+2y+2z=19$
$3x+y+z=14$
If the equations above are true, which of the following is the value of $y+z$ ?

• A. $-5$
• B. $-4$
• C. $0$
• D. $4$
• E. $5$

Answer 1

The correct option is E $5$

Given:

$3x$ $+$ $2y$ $+$ $2z$ $=$ $19$

$3x$ $+$ $y$ $+$ $z$ $=$ $14$

To find the value of $(y$ $+$ $z)$,

Let $(y$ $+$ $z)$ $=$ $t$

From above,

$3x$ $+$ $2$$(y$ $+$ $z)$ $=$ $19$

$\Rightarrow 3x$ $+$ $2t$ $=$ $19$

$\Rightarrow 3x$ $=$ $19$ $-$ $2t$

$\Rightarrow 3x$ $+$ $(y$ $+$ $z)$ $=$ $14$

$\Rightarrow 3x$ $+$ $t$ $=$ $14$

From above two equations, we have

$3x$ $+$ $t$ $=$ $14$

$\Rightarrow 19$ $-$ $2t$ $+$ $t$ $=$ $14$

Rearranging the terms, we get

$t$ $=$ $19$ $-$ $14$

$\Rightarrow t$ $=$ $5$

$\Rightarrow (y$ $+$ $z)$ $=$ $5$

$\Rightarrow y$ $+$ $z$ $=$ $5$

Therefore, the value of $y$ $+$ $z$ is $5$.