Question

MEDALS!
Solve the following system of equations.

4x - 3y + z = -9
x + 2y + 2z = 5
x - 2y + 3z = -2

Answer 1

do you have an idea where to start?

Answer 2

4x - 3y + z = -9
x + 2y + 2z = 5 -->(-4)x + 2y + 2z = 5
---------------
4x - 3y +z = -9
-4x - 8y - 8z = -20 (result of multiplying by -4)
---------------add
0 - 11y - 7z = -29
-11y - 7z = -29

x + 2y + 2z = 5 -->(-1)x + 2y + 2z = 5
x - 2y + 3z = -2
----------------
-x - 2y - 2z = -5 (result of multiplying by -1)
x - 2y + 3z = -2
----------------add
0 - 4y + z = -7
-4y + z = -7

-11y - 7z = -29
-4y + z = -7 -->(7)-4y + z = -7
-----------------
-11y - 7z = -29
-28y + 7z = - 49 (result of multiplying by 7)
-----------------add
-39y + 0 = - 78
-39y = -78
y = -78/-39
y = 2

now sub 2 in for y
-4y + z = -7
-4(2) + z = -7
-8 + z = -7
z = 8 - 7
z = 1

now sub 2 in for y and 1 in for z in one of the original equations
x + 2y + 2z = 5
x + 2(2) + 2(1) = 5
x + 4 + 2 = 5
x + 6 = 5
x = 5 - 6
x = -1

now lets check it....sub in known values
4x - 3y + z = -9
4(-1) - 3(2) + 1 = -9
-4 - 6 + 1 = -9
-10 + 1 = -9
-9 = -9 (correct)

x = -1, y = 2, z = 1 or (-1,2,1)

If you have any questions, please feel free to ask :)