Solve {3x-2y+2z=30, -x+3y-4z=-33, 2x-4y+3z=42}
Please just solve the set provided above!!!!
1) 3x-2y+2z=30
2) -x+3y-4z=-33
3) 2x-4y+3z=42
Equation one; multiply by 2 so the z term has 4 as the coefficient.
3x - 2y + 2z = 30
2 * (3x - 2y + 2z) = 30 * 2
4) 6x - 4y + 4z = 60
Add equation two to equation four:
6x - 4y + 4z = 60
+(-x + 3y - 4z = -33)
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5x - y = 27
5) 5x - y = 27
Multiply equation one by 3. Watch the coefficient of z.
3 * (3x - 2y + 2z) = 30 * 3
6) 9x - 6y + 6z = 90
Multiply equation three by 2. Again, watch the coefficient of z.
2 * (2x - 4y + 3z) = 42 * 2
7) 4x - 8y + 6z = 84
Subtract equation seven from equation six.
9x - 6y + 6z = 90
-(4x - 8y + 6z = 84)
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5x + 2y = 6
8) 5x + 2y = 6
Subtract equation eight from equation five. Both equations
have 5 as the coefficient of x. We eliminate x this way.
5x - y = 27
-(5x + 2y = 6)
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-3y = 21
-3y = 21
y = -7 <<<<<<<<<<<<<<<<<<<
~~~~~~~~~~~~~~~
Plug y into equation five to find x.
5x - y = 27
5x - (-7) = 27
5x + 7 = 27
5x = 27 - 7
5x = 20
x = 4 <<<<<<<<<<<<<<<<<<<
Plug y into equation eight, too.
5x + 2y = 6
5x + 2(-7) = 6
5x - 14 = 6
5x = 6 + 14
5x = 20
x = 4 same value for x
Proceed, solving for the value of z.
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Plug both x and y into equation one. We will
solve for z.
Equation one:
3x - 2y + 2z = 30
3(4) - 2(-7) + 2z = 30
12 + 14 + 2z = 30
26 + 2z = 30
2z = 30 - 26
2x = 4
z = 2 <<<<<<<<<<<<<<<<<<<
Continue using the original equations to
check the values.
Equation two:
-x + 3y - 4z = -33
-(4) + 3(-7) - 4z = -33
-4 - 21 - 4z = -33
-25 - 4z = -33
-4z = -33 + 25
-4z = -8
z = 2 same value for z
Equation three:
2x - 4y + 3z = 42
2(4) - 4(-7) + 3z = 42
8 + 28 + 3z = 42
36 + 3z = 42
3z = 42 - 36
3z = 6
z = 2 satisfied with the results
x = 4, y = -7 and z = 2