substitution x+2y-3z=-13, 4y+2z=2,-x+y-z=-2

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x+2y−3z=−13, 4y+2z=2, −x+y−z=−2

Solution

x=−2, y=−1, z=3

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Solve by substitution

Solve by elimination

Solve by Cramer's rule

Solve by Gaussian elimination

One step at a time

[

x+2y−3z=−13

4y+2z=2

−x+y−z=−2

]

Isolate y for 4y+2z=2: y=1−z2

Substitute y=1−z2

[

x+2· 1−z2 −3z=−13

−x+1−z2 −z=−2

]

Simplify

[

x+1−4z=−13

−x+1−3z2 =−2

]

Isolate x for x+1−4z=−13: x=4z−14

Substitute x=4z−14

[

−(4z−14)+1−3z2 =−2

]

Simplify

[

1−11z2 +14=−2

]

Isolate z for 1−11z2 +14=−2: z=3

For x=4z−14

Substitute z=3

x=4· 3−14

Simplify

x=−2

For y=1−z2

Substitute x=−2, z=3

y=1−32

1−32 =−1

y=−1

The solutions to the system of equations are:

x=−2, y=−1, z=3

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
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substitution x+2y-3z=-13, 4y+2z=2,-x+y-z=-2

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