Solving Three Variable Linear Equation:6x-5z=17 5x-y+3z=-1 2x+y=-41 Solving Three Variable Linear Equation... HELP.... seriously confusing. it will give you a headache.
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`6x-5z=17` -----(1)
`5x-y+3z=-1` ----(2)
`2x+y=-41` ----(3)
`(1)+(3)`
`8x+y-5z = -24` -----(4)
`(2)+(4)` ---> y will cancel out.
`13x-2z = -25 ` ----(5)
`(1)*2-(5)*5` ----> z will cancel out
`12x-65x = 17*2+25*5`
`-53x = 159`
`x = -3`
From (5)
`z = (-25-13*(-3))/(-2) = -7`
From (3)
`y = -41-2*(-3) = -35`
So the answers are;
x = 2
y = -35
z = -7
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The system of equations 6x-5z=17, 5x-y+3z=-1 and 2x+y=-41 has to be solved.
6x-5z=17
=> z = (6x - 17)/5
2x+y=-41
=> y = -41 - 2x
Substitute for z and y in 5x-y+3z=-1
5x + 41 + 2x + 3*(6x - 17)/5 = -1
25x + 205 + 10x + 3*(6x - 17) = -5
25x + 205 + 10x + 18x - 51 = -5
53x = -159
x = -159/53
x = -3
y = -41 - 2x = -41 + 6 = -35
z = (6x - 17)/5 = -35/5 = -7
The solution of the system of equations is x = -3, y = -35 and z = -7
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