Problem: solve following system of equations
solve the following system of equations: x-2y+z=6 , 2x+y-3z=-3, x-3y+3z=10
1) x - 2y + z = 6
2) 2x + y - 3z = -3
3) x - 3y + 3z = 10
Multiply equation 1 by 3.
3(x - 2y + z) = 6 * 3
4) 3x - 6y + 3z = 18
Add equation 2 to equation 4.
3x - 6y + 3z = 18
+(2x + y - 3z = -3)
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5x - 5y = 15
6) 5x - 5y = 15
Add equation 3 to equation 2.
2x + y - 3z = -3
+( x - 3y + 3z = 10)
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3x - 2y = 7
7) 3x - 2y = 7
Multiply equation 6 by 2.
2(5x - 5y) = 15 * 2
8)10x - 10y = 30
Multiply equation 7 by 5.
5(3x - 2y) = 7 * 5
9) 15x - 10y = 35
Subtract equation 9 from equation 8.
10x - 10y = 30
-(15x - 10y = 35)
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-5x = -5
-5x = -5
-5x/-5 = -5/-5
x = 1
Use equation 6 to solve for y.
5x - 5y = 15
5(1) - 5y = 15
5 - 5y = 15
5 - 5y - 5 = 15 - 5
-5y = 10
-5y/-5 = 10/-5
y = -2
Use equation 3 to solve for z.
x - 3y + 3z = 10
1 - 3(-2) + 3z = 10
1 + 6 + 3z = 10
7 + 3z = 10
3z = 3
3z/3 = 3/3
z = 1
Answer: x = 1, y = -2, z = 1