algebra question?

Question

solve the following equation using the substitution method only.

3x + 4y - z = 2
2x - 3y + z = -5
5x -2y + 2z = -3

im pretty confused on how to use substitution with three variables, can someone please help?

Answer 1

You have to use it twice. First, let's get rid of z. From the second equation we can write
z = 3y - 2x - 5
so substitute this into BOTH the other equations:
3x + 4y - (3y - 2x - 5) = 2
5x - 2y + 2(3y - 2x - 5) = -3

Simplifying these gives you:
5x + y = -3
x + 4y = 7

Now use substitution on these to solve for x and y, then plug those back into the equation we used earlier (z = 3y - 2x - 5) to find z. You should get x = -1, y = 2, z = 3.

Answer 2

3x + 4y - z = 2(1)
2x - 3y + z = -5(2)
5x -2y + 2z = -3(3)

(1)+(2)<=>(3x+4y-z)+(2x-3y+z)=2+(-5)
<=>5x+y= -3 (4)

(2)<=>4x-6y+2z=-10 (5)

(3)-(5)<=>(5x -2y + 2z)-(4x-6y+2z)= -3-(-10)
<=>x+4y=7
<=>5x+20y=35(6)

(4)-(6)<=>(5x+y)-(5x+20y)=-3-35
<=>-19y= -38
<=>y=2(7)
(4)and(7)=>5x= -3-y= -5=>x= -1(8)
(1)=>z=3x+4y-2= -3+8-2=3

x=1;y=2;z=3