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I need help with my homework (solving systems of equations)

I need help with my homework (solving systems of equations)-example-1
User Timothyylim
by
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1 Answer

20 votes
20 votes

The equation has no solution

Step-by-step explanation:

2x - y + 3z = 1 ...(1)

5x + 2y - 2z = 4 ...(2)

-7x - y - z = -5 ...(3)

Using eliminaton method:

Let's eliminate y. We need to ensure the coefficient of y is the same

To do this, we multiply equation (1) by 2:

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

4x - 2y + 6z = 2 ...(1b)

Then we Add equation (1b) and (2):

4x - 2y + 6z = 2 ...(1b)

5x + 2y - 2z = 4 ...(2)

5x + 4x + 2y + (-2y) -2z + (6z) = 4 + 2

9x + 0 + 4z = 6

9x + 4z = 6 ...(4)

Multiply equation (3) by 2:

2(-7x) -2(y) -2(z) = 2(-5)

-14x - 2y - 2z = -10 ...(3b)

add equation (2) and (3b) to eliminate y:

5x + (-14x) + 2y + (- 2y) - 2z + (-2z) = 4 + (-10)

-9x + 0 -4z = -6

-9x - 4z = -6 ...(5)

We solve equaion (4) and (5) simultaneously:

9x + 4z = 6 ...(4)

-9x - 4z = -6 ...(5)

Let's eliminate x by adding both equations together:

9x + (-9x) + 4z + (-4z) = 6 + (-6)

0 + 0 = 0

The equation has no solution

User Tuncay
by
2.8k points