Question 1203437
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Solve the 1st equation for z.
3x+6y-z = 7
3x+6y = 7+z
3x+6y-7 = z
z = 3x+6y-7


Plug this into the 2nd equation.
2x-3y+5z = -12
2x-3y+5(3x+6y-7) = -12
2x-3y+15x+30y-35 = -12
17x+27y-35 = -12
17x+27y = -12+35
17x+27y = 23


Do the same for the 3rd equation.
8x+9y-2z=12
8x+9y-2(3x+6y-7)=12
8x+9y-6x-12y+14=12
2x-3y+14=12
2x-3y=12-14
2x-3y=-2


The task is now to solve this reduced system
17x+27y = 23
2x-3y = -2


We can solve for x in the equation 2x-3y = -2 to get x = 1.5y-1
Then plug this into the other equation to solve for y
17x+27y = 23
17(1.5y-1)+27y = 23
25.5y-17+27y = 23
52.5y-17 = 23
52.5y = 23+17
52.5y = 40
y = 40/52.5
y = 400/525
y = 16/21


Use this value of y to find x.
Then use the values of x and y to find z.


I'll let the student take over from here.
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