Question 1127836

Solve the of equation 2x-y+z=-7, x-3y+4z=-19, and -x+4y-3z=18.

A. There is one solution (-1,2,-3)
B. There is one solution (1,-2,3)
C. There is one solution (-1,-2,-3)
D. There is one solution (1,2,3)
<pre>2x - y + z = - 7 -------- eq (i)
x - 3y + 4z = - 19 ------ eq (ii)
- x + 4y - 3z = 18 ------ eq (iii)
        y + z = - 1 -------- Adding eqs (iii) & (ii) ------ eq (iv)
- 2x + 8y - 6z = 36 -------- Multiplying eq (iii) by 2 ------ eq (v)
       7y - 5z = 29 -------- Adding eqs (v) & (i) ------ eq (vi)
       5y + 5z = - 5 ------- Multiplying eq (iv) by 5 ------ eq (vii)
12y = 24 ------ Adding eqs (vii) & (vi)
{{{highlight_green(matrix(1,5, y, "=", 24/12, "=", 2))}}}
2 + z = - 1 ------ Substituting 2 for y in eq (iv)
{{{highlight_green(matrix(1,5, z, "=", - 1 - 2, "=", - 3))}}}
2x - 2 + - 3 = - 7 ------ Substituting 2 for y, and - 3 for z in eq (i)
2x - 5 = - 7
2x = - 7 + 5
2x = - 2
{{{highlight_green(matrix(1,5, x, "=", (- 2)/2, "=", - 1))}}}
Now, you choose the correct answer!