Question 193815
Solve for x only
4x + 2y + z = 24
2x - 3y - z = 2
5x + y + 2z = 21
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Eliminate z
Add the 1st and 2nd eqn
4x + 2y + z = 24
2x - 3y - z = 2
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6x - 1y = 26  eqn A
Multiply the 2nd eqn by 2, then add the 3rd.
4x - 6y -2z = 4
5x + y + 2z = 21
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9x - 5y = 25  eqn B
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Now you have 2 eqns in 2 unknowns, not 3.
Multiply eqn A by 5 and subtract eqn B.
30x - 5y = 130  eqn A times 5
9x - 5y = 25  eqn B
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21x = 105
x = 5