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

The answer is E

Explanation:

Before we find the value of 5, let's find x by using the elimination process for the two given equation.

2(3x + y + z = 14) → 6x + 2y + 2z = 28

3x + 2y + 2z = 19

-6x + 2y + 2z = 28

-3x = -9

x = 3

Now plug in 3 into both of the given equations, which will give you your new equation, then subtract them:

3(3) + 2y + 2z = 19 → 9 + 2y + 2z = 19

3(3) + y + z = 14 →   - 9 + y + z = 14

Our answer is: y + z = 5

Our value is 5

Optional: If you want to make sure it's 5, plug-in any random numbers for y and z that equals 5. For example: 3 + 2, 1 + 4, 5 + 0, 6 + (-1), etc...

Once you choose the numbers you can plug them into the two new given equations. For me, I decided to let y = 1 and z = 4:

9 + 2(1) + 2(4) = 19     9 + (1) + (4) = 14

9 + 2 + 8 = 19            9 + 1 + 4 = 14

19 = 19                       14 = 14

it was like a 9