What is the solution of the system of equations? {3x+2y+z=7 {5x+5y+4z=3 {3x+2y+3z=1
2 answers:
Answer:
(x, y, z) = (4, -1, -3)
Step-by-step explanation:
A graphing calculator and many scientific calculators can solve this for you. Web sites will solve these for you, too.
If you want to do it by hand, you can subtract the first equation from the third to find z:
(3x +2y +3z) -(3x +2y +z) = (1) -(7)
2z = -6
z = -3
Substituting this into the second equation gives ...
5x +5y +4(-3) = 3
5x +5y = 15
Multiplying this by 2/5, you get ...
2x +2y = 6
and subtracting this from the first equation gives ...
(3x +2y -3) -(2x +2y) = (7) -(6)
x -3 = 1
x = 4
Putting this into the equation for x and y above gives ...
2(4) +2y = 6
y = -2/2 = -1 . . . . . subtract 8 and divide by 2
Then the solution is (x, y, z) = (4, -1, -3).
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