Question 709251
eq 1 2x + y + z = 0 
eq 2 3x - y + z = 3 
Eq 3 7x - 5y - 3z = 15

Add eq 1 and eq 2: 5x + 2z = 3 and z = 1/2[3 - 5x] eq 4

Subtract eq 1 from eq 2; x - 2y = 3 and y = 1/2[x - 3] eq 5

Substitute eq 4 and eq 5 into eq 3 giving:

7x - 5[1/2(x - 3)] - 3[1/2(3 - 5x)] = 15

Multiply both sides of this equation by 2 to eliminate the fractions and simplify the resulting equation by adding like terms. Isolate the variable x to the left side of the equation. 

14x - 5x + 15 - 9 + 15x = 30

24x = 24

x  = 1

From eq 4 we have z = 1/2(3 - 5(1)] = -1
From eq 5, we have y = 1/2[1 - 3] = -1

The solution is (x, y, z) = (1, -1, -1).