Question

can someone help me with this system of equations?

Answer 1

3x + 2y + z = 7 ---->(5)
5x + 5y + 4z = 3 --->(-3)
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15x + 10y + 5z = 35 (result of multiplying by 5)
-15x - 15y - 12z = -9 (result of multiplying by -3)
---------------add
-5y - 7z = 26

5x + 5y + 4z = 3 --->(-3)
3x + 2y + 3z = 1---->(5)
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-15x - 15y - 12z = -9 (result of multiplying by -3)
15x + 10y + 15z = 5 (result of multiplying by 5)
-------------add
-5y + 3z = - 4

-5y - 7z = 26 --->(-1)
-5y + 3z = -4
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5y + 7z = -26 (result of multiplying by -1)
-5y + 3z = -4
-----------add
10z = - 30
z = -30/10
z = -3

-5y - 7z = 26
-5y - 7(-3) = 26
-5y + 21 = 26
-5y = 26 - 21
-5y = 5
y = 5/-5
y = -1

3x + 2y + z = 7
3x + 2(-1) + (-3) = 7
3x - 2 - 3 = 7
3x - 5 = 7
3x = 7 + 5
3x = 12
x = 12/3
x = 4

check...
5x + 5y + 4z = 3
5(4) + 5(-1) + 4(-3) = 3
20 - 5 - 12 = 3
20 - 17 = 3
3 = 3 (correct)

x = 4, y = -1, and z =-3..........(4,-1,-3)