Use Gaussian elimination and a matrix with row operations to solve the system. Give the value of y.

Question

-2x + 3y - z = -9

2x + y - 2z = 2

2x - 2y - z = 11

Answer 1

-2x + 3y - z = -9

2x + y - 2z = 2

2x - 2y - z = 11

Creating a 3x4 matrix of the above values, solving using RREF yields

x= 0

y=-4

z=-3

Answer 2

Equation #1 + Equation #2

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4y - 3z = -7

Equation #1 + Equatino #3

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y - 2z = 2

4y - 3z = -7

y - 2z = 2

-4 * eq 2 + eq 1

5z = -15

z = -3

y - 2(-3) = 2

y + 6 = 2

y = -4

original 2nd equation:

2x + y - 2z = 2

2x - 4 - 2(-3) = 2

2x - 4 + 6 = 2

2x + 2 = 2

2x = 0

x = 0

x=0, y= -4, z = -3