Problem: How do I find the solution for this system of equations 6x - 2y - z = -21
6x - 2y - z = -21 3y + 4z = 2 2x + 5y - 3z = 7
1) 6x - 2y - z = -21
2) 3y + 4z = 2
3) 2x + 5y - 3z = 7
Multiply equation 1 by 4.
4(6x - 2y - z) = -21 * 4
4) 24x - 8y - 4z = -84
Add equation 2 to equation 4.
24x - 8y - 4z = -84
+( 3y + 4z = 2)
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24x - 5y = -82
5) 24x - 5y = -82
Multiply equation 2 by 3.
3(3y + 4z) = 2 * 3
6) 9y + 12z = 6
Multiply equation 3 by 4.
4(2x + 5y - 3z) = 7 * 4
7) 8x + 20y -12z = 28
Add equation 7 to equation 6.
9y + 12z = 6
+(8x + 20y - 12z = 28)
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8x + 29y = 34
8) 8x + 29y = 34
Multiply equation 5 by 29.
29(24x - 5y) = -82 * 29
9) 696x - 145y = -2378
Multiply equation 8 by 5.
5(8x + 29y) = 34 * 5
10) 40x + 145y = 170
Add equation 10 to equation 9.
696x - 145y = -2378
+(40x + 145y = 170)
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736x = -2208
736x = -2208
x = -3
Use equation 5 to solve for y.
24x - 5y = -82
24(-3) - 5y = -82
-72 - 5y = -82
-5y = -10
y = 2
Use equation 3 to solve for z.
2x + 5y - 3z = 7
2(-3) + 5(2) - 3z = 7
-6 + 10 - 3z = 7
4 - 3z = 7
-3z = 3
z = -1
ANSWER: x = -3, y = 2, z = -1