SOLUTION: Hello I have a substitution problem with 3 equations, there are no examples in my text for a 3 equation using the substitution method to solve when there are missing variables in s

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Question 106763: Hello I have a substitution problem with 3 equations, there are no examples in my text for a 3 equation using the substitution method to solve when there are missing variables in some of them
3x + z=9
x + 3y =5
2x - y +2z=9
I have tried everything possible but I just cannot come up with a solution. Can you please help me out?
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Solve:
1) 3x+z = 9 Rewrite this as: z = -3x+9 and substitute into equation 3)
2) x+3y = 5
3) 2x-y+2z = 9
3a) 2x-y+2(-3x+9) = 9 Simplify.
3a) 2x-y-6x+18 = 9
3a) -4x-y = -9 Now multiply this equation by 3 and add it to equation 2)
3b)-12x-3y = -27
2) x+3y = 5
----------------
-11x =-22
x = 2 Substitute this into equation 1) and solve for z.
1) 3(2)+z = 9
6+z = 9
z = 3 Finally, substitute x = 2 and z = 3 into equation 3) and solve for y.
3) 2(2)-y+2(3) = 9
4-y+6 = 9
10-y = 9
y = 10-9
y = 1
Solution:
x = 2
y = 1
z = 3