Denise G. answered • 03/17/19
Algebra, College Algebra, Prealgebra, Precalculus, GED, ASVAB Tutor
If you add the first 2 equations together, the result is 3x+2z=18 (the y terms are the same coefficients, opposite signs so they sum to zero.
You can use this equation along with the last equation which is already in terms of x and z
3x+2z=18
3x-z=9
This is 2 equations and 2 unknowns that can be solved by elimination. (or substitution- I used elimination)
Multiply the second equation by -1
-1(3x-z=9) = -3x+z=-9
3x+2z=18 (same)
-3x+z=-9
Add the 2 equations together to get
3z=9
Divide both sides by 3
z=3
Using the 3rd equations you can plug in z and solve for x
3x-z=9
3x-3=9
Add 3 to both sides
3x=12
Divide both sides by 3
x=4
Use the first equation (you can use 1st or second but the first is easier)
x+y+z=8
Plug in x and z that you already solved for
4+y+3=8
Combine like terms
7+y=8
Subtract 7 from both sides
y=1
The solution is (4,1,3)
