The equation has no solution
Step-by-step explanation:
2x - y + 3z = 1 ...(1)
5x + 2y - 2z = 4 ...(2)
-7x - y - z = -5 ...(3)
Using eliminaton method:
Let's eliminate y. We need to ensure the coefficient of y is the same
To do this, we multiply equation (1) by 2:
2(2x) - 2(y) + 2(3z) = 2(1)
4x - 2y + 6z = 2 ...(1b)
Then we Add equation (1b) and (2):
4x - 2y + 6z = 2 ...(1b)
5x + 2y - 2z = 4 ...(2)
5x + 4x + 2y + (-2y) -2z + (6z) = 4 + 2
9x + 0 + 4z = 6
9x + 4z = 6 ...(4)
Multiply equation (3) by 2:
2(-7x) -2(y) -2(z) = 2(-5)
-14x - 2y - 2z = -10 ...(3b)
add equation (2) and (3b) to eliminate y:
5x + (-14x) + 2y + (- 2y) - 2z + (-2z) = 4 + (-10)
-9x + 0 -4z = -6
-9x - 4z = -6 ...(5)
We solve equaion (4) and (5) simultaneously:
9x + 4z = 6 ...(4)
-9x - 4z = -6 ...(5)
Let's eliminate x by adding both equations together:
9x + (-9x) + 4z + (-4z) = 6 + (-6)
0 + 0 = 0
The equation has no solution