2x-6y+6z=17, x+2y-3z=13, 3x+21z=26
am trying to find what the x , y , and z value of the equation would be
1) 2x - 6y + 6z = 17
2) x + 2y - 3z = 13
3) 3x + 21z = 26
Equation 3 is missing a y term, so let's work with
equations 1 and 2 to eliminate the y term.
Multiply equation 2 by 3.
3 * (x + 2y - 3z) = 13 * 3
4) 3x + 6y - 9z = 39
Add equation 4 to equation 1.
2x - 6y + 6z = 17
+(3x + 6y - 9z = 39)
--------------------------
5x - 3z = 56
5) 5x - 3z = 56
Multiply equation 5 by 7.
7 * (5x - 3z) = 56 * 7
6) 35x - 21z = 392
Add equation 6 to equation 3.
3x + 21z = 26
+(35x - 21z = 392)
-----------------------
38x = 418
38x = 418
x = 11 <<<<<<<<<<<<<<<<<<<<
Plug that right back into equation 3 and solve for z.
3x + 21z = 26
3(11) + 21z = 26
33 + 21z = 26
21z = -7
z = -7/21
z = -1/3 <<<<<<<<<<<<<<<<<<<<
Use equation 2 to solve for y.
x + 2y - 3z = 13
11 + 2y - 3(-1/3) = 13
11 + 2y + 1 = 13
12 + 2y = 13
2y = 1
y = 1/2 <<<<<<<<<<<<<<<<<<<<
Of course, we have to check those values by
plugging them into equation 1.
2x - 6y + 6z = 17
2(11) - 6(1/2) + 6(-1/3) = 17
22 - 3 - 2 = 17
17 = 17
x = 11, y = 1/2, z = -1/3