This is a 3 variable linear equation problem, that I am not sure how to combine to solve. The problem is to solve the system using linear combination method. Here are the three equations:
5x-4y+4z=18
-x+3y-2z=0
4x-2y+7z=3
I have combined the first and second problem to eliminate z, but I don't know what to do from there.
First I distibuted a scale of 2 to the second problem so that the z's would cancel out, and then I solved.
(2)-x+3y-2z=0
-2x+6y-4z=0
5x-4y+4z=18
+ -2x+6y-4z=0
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3x+2y =18
Please help me eliminate another variable so I can solve the rest of the problem.
The easiest variable to eliminate is x. You do this by MULTIPLYING equation 2 by 5 to create equation (iv).
Then subtract equation (iv) from equation (i). You now have an equation in 2 unknowns (y and z). This is equation (v)
You then MULTIPLY equation 2 by 4 to create equation (vi). Then subtract equation (vi) from equation (iii).
You now have an equation in 2 unknowns (y and z). This is equation (vii)
Eliminate one of the variables from equations (v) and (vii). When you have 1 equation in 1 unknown,
and solve for that unknown, you will then be able to determine the values for the other 2 variables.
When all is "said and done," you should obtain:
You can do the check!!
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