Using the method of elimination: Adding equation (2) and (3): (x-3y+4z)+(-x+4y-3z)=(-19)+(18) x-3y+4z-x+4y-3z=-19+18 y+z=-1 Solving for z: y+z-y=-1-y z=-1-y
Multiplying the third equation by 2: (3) -x+4y-3z=18 2(-x+4y-3z=18) -2x+8y-6z=36 Adding with equation (1) (2x-y+z)+(-2x+8y-6z)=(-7)+(36) 2x-y+z-2x+8y-6z=-7+36 7y-5z=29 Replacing z=-1-y in the equation above: 7y-5(-1-y)=29 7y+5+5y=29 12y+5=29
Solving for y. Subtracting 5 both sides of the equation. 12y+5-5=29-5 12y=24 Dividing both side of the equation by 12: 12y/12=24/12 y=2
Replacing y=2 in z=-1-y z=-1-2→z=-3
Replacing y=2 and z=-3 in the equation (2); and solving for x: (2) x-3y+4z=-19 x-3(2)+4(-3)=-19 x-6-12=-19 x-18=-19 Adding 18 both sides of the equation: x-18+18=-19+18 x=-1
There is one solution: (x,y,z)=(-1,2,-3)
Answer: Option <span>D. There is one solution (–1, 2, –3).</span>
