Pre Cal.Check my work?
posted by David .
Solve the system of equations: x  y  z = 2; x + 2y  2z = 3; 3x  2y  4z = 5?
well, you have:
1 xyz=2
2 x+2y2z=3
3 3x2y4z=5
multiply both sides of the equation 1 by 2:
xyz=2 ===> 2x2y2z=4
add this by equation 2:
2x2y2z=4
x+2y2z=3
==> 3x  4z = 7 (*)
now, multiple both sides of equation 1 by 2:
xyz=2
==> 2x + 2y + 2z = 4
add this by equation 3:
2x + 2y + 2z = 4
3x2y4z=5
===> x  2z = 1
great. now you have
x  2z = 1
and
3x  4z = 7
so , multiple both sides of the first one by 2:
2x + 4z = 2
3x  4z = 7
===> (add them together) x = 5
3x  4z = 7 ===(x=5)=> 15  4z = 7 ==> 4z = 8 ==> z=2
xyz= 2 ===> 5y2 = 2 ==> y=1
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