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Need help with number five. The question is solve each system

Need Help With Number Five The Question Is Solve Each System class=

Sagot :

5)

The given equations are

- 4x - 2y + 3z = 7

- 3x + 5y - 3z = 13

- 5x + y - z = 11

From equation 3, we have

y = 11 + 5x + z

We would substitute y = 11 + 5x + z into equations 1 and 2. For equation 1, we have

- 4x - 2(11 + 5x + z) + 3z = 7

- 4x - 22 - 10x - 2z + 3z = 7

- 4x - 10x - 2z + 3z = 7 + 22

- 14x + z = 29

For equation 2, we have

- 3x + 5(11 + 5x + z) - 3z = 13

- 3x + 55 + 25x + 5z - 3z = 13

- 3x + 25x + 5z - 3z = 13 - 55

22x + 2z = - 42

Dividing both sides of the equation by 2, we have

11x + z = - 21

z = - 21 - 11x

Substituting z = - 21 - 11x into - 14x + z = 29, we have

- 14x - 21 - 11x = 29

- 14x - 11x = 29 + 21

- 25x = 50

x = 50/- 25

x = - 2

z = - 21 - 11(- 2) = - 21 + 22

z = 1

Substituting x = - 2 and z = 1 into y = 11 + 5x + z, we have

y = 11 + 5(-2) + 1

y = 11 - 10 + 1

y = 2

The solutions are

x = - 2, y = 2, z = 1

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