SOLUTION: 5.8 Solve the given system of equations 5x+2y-5z=11 2x-5y+2z=-1 4x-3y+4z=19 The solution set is { } I got {4,3,3} is this correct?

Question 1014507: 5.8
Solve the given system of equations
5x+2y-5z=11
2x-5y+2z=-1
4x-3y+4z=19
The solution set is { }
I got {4,3,3} is this correct?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
you are correct
**************************************************
1) 5x +2y -5z = 11
2) 2x -5y +2z = -1
3) 4x -3y +4z = 19
*************************************************
multiply 2) by 2 and subtract from 3)
7y = 21
y = 3
*************************************************
substitute for y in 1) and 2)
5x +6 - 5z = 11
5x -5z = 5
x - z = 1
:
2x -15 + 2z = -1
2x +2z = 14
x + z = 7
*********************************************
solve first for x
x = z+ 1
now substitute for x in second
z+1 +z = 7
2z = 6
z = 3
********************************************
now substitute for y=3 and z=3 in equation 1)
5x +6 -15 = 11
5x = 20
x = 4
*********************************************
solution set is (4, 3, 3)

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