Please please help

Question

Solve for z:

x = 2.5y

x + y + z = 66

x - 2y - 2z = -12

(A) z = -120

(B) z = 16

(C) z = 10

(D) z = -74

(E) None of these

Answer 1

Given:

Eq-1: x = 2.5y

Eq-2: x + y + z = 66. Multiply this equation throughout by 2: 2x + 2y + 2z = 66*2 = 132. (66 multiplied by 2)

Eq-3: x - 2y - 2z = -12.

Now we have:

2x + 2y + 2z = 132.

x - 2y - 2z = -12. (this is eq-3)

Notice the 2y & -2y; and 2z & -2z terms. If you add these two equations, these terms will get cancelled. Then we are left with 2x + x on the left side of the equation. On the right side, it will be 132 - 12 = 120.

Adding above equations, we get: 3x = 120. So x = 120/3 = 40. x = 40

x = 2.5y (this is given equation -1). So y = x/2.5 = 40/2.5 = 40/(5/2) = 16. y = 16

Equation-2 is given to us: x + y + z = 66.

x=40, y=16. Substitute: 40 + 16 + z = 66. So z = 66 - 40 - 16 = 10. Hence z = 10

Answer is C

Answer 2

Substitute for x in the 2nd and 3rd equations to get

3.5y+z=66

.5y-2z=-12

Multiply the 2nd of these 2 equations by 7 and subtract to eliminate y.

This will give you a simple equation in z alone....and your answer.

Answer 3

Hi!

Since we are only looking for z, all we have to do is cancel out the x and y terms. The first step to this is to plug in x = 2.5y to both the equations x + y + z = 66 and x - 2y - 2z = -12 and then combine the y terms. Doing this, we get 3.5y + z = 66, and 0.5y - 2z = -12. The next step is to then multiply the equations by constants to get the y terms equal so we can cancel them. For example, we would multiply 3.5y + z = 66 by 2 on both sides, and 0.5y - 2z = -12 by 14 on both sides.

This gives us 7y + 2z = 132, and 7y - 28z = -168. Now we can subtract one equation from the other to leave us with just the z terms. Subtracting 7y - 28z = -168 from 7y + 2z = 132 we get 30z = 300. Now we can divide both sides by 30, leaving us with z = 10.

Therefore, C: z = 10 is the correct answer.

Answer 4

x+y +z = 66

mulriply by 2

2x+2y +2z= 132

x-2y -2z =-12

add to get

3x = 120

x=120/3 =40

y =40/2.5 = 16

z = 66-40-16 = 10

z=10

C) is correct

you can solve by substitution & elimination or matrix algebra

or just try out each value of z until one works: A), B), C), D) and E)

C) works using z=10