find the ordered triple of these equations.
x-2y+2z=-2
2x+3x-z=0
3x+2x+3z=-15
1) x - 2y + 2z = -2
2) 2x + 3x - z = 0
3) 3x + 2y + 3z = -15 ---- surely that's 2y, not 2x
Multiply equation 2 by 2.
2(2x + 3x - z) = 0 * 2
4) 4x + 6y - 2z = 0
Add equation 4 to equation 1.
x - 2y + 2z = -2
+(4x + 6y - 2z = 0)
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5x + 4y = -2
5) 5x + 4y = -2
Multiply equation 2 by 3.
3(2x + 3y - z) = 0 * 3
6) 6x + 9y - 3z = 0
Add equation 3 to equation 6.
6x + 9y - 3z = 0
+(3x + 2x + 3z = -15)
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9x + 11y = -15
7) 9x + 11y = -15
Multiply equation 5 by 11.
11(5x + 4y) = -2 * 11
8) 55x + 44y = -22
Multiply equation 7 by 4.
4(9x + 11y) = -15 * 4
9) 36x + 44y = -60
Subtract equation 9 from equation 8.
55x + 44y = -22
-(36x + 44y = -60)
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19x = 38
19x = 38
x = 2 <<<<<<<<<<<<<<<<
Use equation 5 to solve for y.
5x + 4y = -2
5(2) + 4y = -2
10 + 4y = -2
4y = -12
y = -3 <<<<<<<<<<<<<<<<
Use equation 3 to solve for z.
3x + 2y + 3z = -15
3(2) + 2(-3) + 3z = -15
6 - 6 + 3z = -15
3z = -15
z = -5 <<<<<<<<<<<<<<<<
Check the answer with equation 1.
2 - 2(-3) + 2(-5) = -2
2 + 6 - 10 = -2
8 - 10 = -2
-2 = -2
Answer: x = 2, y = -3, z = -5