Question

What is the solution to the following system? X+2y+z=9 X-y+3z=13 2z=10

Answer 1

Answer:  x = 0; y = 2; z = 5

Step-by-step explanation:

x+2y+z=9

x-y+3z=13

2z=10

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Start with the last equation:  2z = 10, therefore z = 5 [easy]

Let's rewrite the second equation with 1) z=5, and 2) rearrange to find x:

x-y+3z = 13

x - y +3*5 = 13

x = y-2

Now use the values for x [(y-2)] and y [5] in the first equation:

X+2y+z=9

(y-2) +2y + 5 = 9

3y +3 = 9

3y = 6

y = 2

Now that we have y [2] and z [5], let's use the first equation to solve for x:

x+2y+z=9

x + 4 + 5 = 9

x + 9 = 9

x = 0

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Try the three values (x=0, y=2, and z=5) in any of the formulas.  The result should/will equal the number shown.