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# 1. What is the solution to the system of equations?

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1. What is the solution to the system of equations?

{−2x + 6y = −38

3x − 4y =

A.(4, −5)

B.(−5, 4)

C.(1, −6)

D. (−4, −5)

2.What is the solution to the system of equations?

x + 3y − z = 6

4x − 2y + 2z = −10

6x + z = −12

A. (−4, 0, 12)

B. (−3, 5, 6)

C. (2, 1, −3)

D. (0, −2, −12)

Dec 12, 2017

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2.

 ___ ___ ____ ________________________________ ___ ___ ____ x + 3y - z = 6 multiply through by  2  to get 2x + 6y - 2z = 12 4x - 2y + 2z = -10 multiply through by  3  to get 12x - 6y + 6z = -30 6x + z = -12 multiply through by -4  to get -24x - 4z = 48

Add these three equations together to get

-10x   =   30             Divide both sides by  -10 .

x   =   -3

Use this value for  x  in the third given equation to find  z .

6(-3)  +  z   =   -12             Subtract  6(-3)  from both sides.

z   =   -12 - 6(-3)   =   -12 + 18   =   6

Now we can find  y  using the first given equation.

-3  +  3y  -  6   =   6

3y   =   15

y   =   5

So    x  =  -3 ,    y  =  5 ,    and    z  =  6

Dec 12, 2017