Question

In the system below, use equation (1) with equation (2) to eliminate x. Then use equation (1) with equation (3) to eliminate x. x-y-2z=4 (1) -x+3y-z=8 (2) -2x-y-4z=-1 (3) What is the new 2 × 2 system?

Answer 1

2y - 3z = 12.

-3y - 8z = 7.

Explanation:

x - y - 2z = 4 (1)

-x + 3y - z = 8 (2)

-2x - y - 4z = -1 (3)

Adding (1) + (2):

2y - 3z = 12.

2 * (1) + (3) gives:

-3y - 8z = 7.

Answer 2

• 2y -3z = 12
• -3y -8z = 7

Explanation:

(1) +(2) ⇒ (x -y -2z) +(-x +3y -z) = (4) +(8)

2y -3z = 12

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2(1) +(3) ⇒ 2(x -y -2z) +(-2x -y -4z) = 2(4) +(-1)

-3y -8z = 7

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The reduced system of equations is ...

• 2y -3z = 12
• -3y -8z = 7