Answer: x = 5
y = 2
z = 2
Explanation:
-3x+4y+2z=-3 - ,- - - - - - 1
2x-4y-z=0 - - - - - - - - - - 2
y=3x-13 - - - - - - - - - - 3
We will use the method of substitution.
Substituting y = 3x -13 into equation 1 and equation 2, it becomes
-3x+4(3x-13)+2z=-3
-3x + 12x - 52 + 2z=-3+52
9x+2z = 49 - - - - - - -4
2x - 4(3x-13)-z= 0
2x - 12x + 52 - z = 0
-10x- z = -52 - - - - - - --5
Using elimination method to solve equation 4 and equation 5
Multiply equation 5 by 2 and equation 4 by 1
-20x - 2z = -104
9x+2z = 49
Adding both equations,
-11x = -55
x = -55/-11
x = 5
Substituting x = 5 into equation 3
y = 3x - 13
y = 3×5 -13 = 15-13
y = 2
Substituting x = 5 and y = 2 into equation 1,
-3x+4y+2z=-3
-3×5 + 4×2 +2z = -3
-15+8+2z = -3
-7+2z = -3
2z = -3+7
2z = 4
z = 4/2 = 2