Question

Solve system of equations0%3D%208%20%5C%5C%20%20-%202x%20%2B%203y%20-%202z%20%3D%2010" id="TexFormula1" title="x + 2y - z = 4 \\ 2x - y + 3z = 8 \\ - 2x + 3y - 2z = 10" alt="x + 2y - z = 4 \\ 2x - y + 3z = 8 \\ - 2x + 3y - 2z = 10" align="absmiddle" class="latex-formula">

Answer 1

First, using elimination method for eq. 1 and 2 to eliminate one of the variables.

2x - y + 3z = 8

-2x + 3y - 2z = 10

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2y + z = 18

z = 18 - 2y

Now eq. 1 and 3, but multiple eq.1 with 2.

2x + 4y - 2z = 8

-2x + 3y - 2z = 10

----------------------------

7y - 4z = 18

Now you have two new equations 7y -4z = 18 and z = 18 - 2y. Solve for y and z, using substitute method.

7y - 4z = 18

7y - 4(18 - 2y) = 18

7y - 72 + 8y = 18

15y = 18+72

y = 90/15

y = 6

Find z using one of the two new equations.

z = 18 - 2y

z = 18 - 2(6)

z = 18 - 12

z = 6

Now you got y and z, find x using any one of the main three equations.

x + 2y - z = 4

X + 2(6) - 6 = 4

x + 12 - 6 = 4

x = 4 - 6

x = -2

Solutions:

x = -2

y = 6

z = 6