Question

What is the solution of the system? Use elimination. Check your answer in all three original equations.

Answer 1

By elimination, the solution of the system of equations, x - y + z = -1, x + y + 3z = -3 and 2x - y + 2z = 0, is  (4 , 2 , -3).

Given:

x - y + z = -1     (equation 1)

x + y + 3z = -3     (equation 2)

2x - y + 2z = 0     (equation 3)

Using the elimination method, given the equations in x, y, and z, a variable should be eliminated by adding/subtracting the equations.

Subtracting equations 1 and 3 will eliminate the variable y.

2x - y + 2z = 0     (equation 3)

 x - y + z = -1   (equation 1)

x        + z = 1     (equation 4)

Adding equations 2 and 3 will eliminate the variable y.

x + y + 3z = -3     (equation 2)

2x - y + 2z = 0     (equation 3)

3x      + 5z = -3     (equation 5)

Multiply equation 4 by -5 and add with equation 5.

x + z = 1     (equation 4)

⇒ -5x - 5z = -5

+    3x + 5z = -3     (equation 5)

-2x             = -8

x = 4

Substitute the value of x to either equation 4 or 5 and solve for z.

x + z = 1     (equation 4)

4 + z = 1

z = 1 - 4

z = -3

Finally, substitute the value of x and z to any of the first three equations, and solve for y.

x - y + z = -1     (equation 1)

4 - y + (-3) = -1

-y = -1 - 4 + 3

-y = -2

y = 2

Checking if the values x = 4, y = 2, and z = -3 satisfies all the three equation.

x - y + z = -1     (equation 1)

4 - 2 + (-3) = -1

-1 = -1

x + y + 3z = -3     (equation 2)

4 + 2 + 3(-3) = -3

-3 = -3

2x - y + 2z = 0     (equation 3)

2(4) - 2 + 2(-3) = 0

0 = 0

Hence, the solution of the system of equations is (4 , 2 , -3).

Learn more about solving systems of equations by elimination here: brainly.com/question/28405823

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