Question

Solve the following system of equations.

x + 2y - 6 = z
3y - 2z =7
4 + 3x = 2y - 5z

Answer 1

x = 7/4
y = 3/2
z = -5/4
Step 1: Multiply first equation by

−3 and add the result to the third equation. The result is:

x+ 2 y+ 3 y− 8 y− z− 2 z+ 8 z = 6 = 7 = −22

Step 2: Multiply second equation by 4 and add the result to the third equation. The result is:

x+ 2 y+ 3 y+ 4 y− z− 2 z = 6 = 7 = 6

Step 3: solve for y.

4 yy=6=32

Step 4: solve for z.

3z−2z3⋅32−2zz=7=7=−54

Step 5: solve for x by substituting y=32 and z=−54 into the first equation.

Answer 2

Answer:x=
`(7)/(4)`

y=
`(3)/(2)`

z=
`-(5)/(4)`

Explanation:

The given equations are

x + 2y - 6 = z (1)

3y - 2z =7 or 3y=2z+7 (2)

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

Equation 3 can be rewritten as 3x-2y =-5z-4 (4)

Equation 1 can be rewritten as x+2y=z+6 (5)

Adding the two equations we have: ----------------

4x =-4z+2

or x= -z+0.5 (6)

Multiplying equation (5 ) by 3 and equation (2) by 2 so that y can be eliminated we have:

3x+6y=3z+18

6y = 4z+14

................................

3x = -z+4 ( subtracting the two equations)

substituting x value from equation (6) we have:

3(-z+0.5) =-z+4

Or,-3z+1.5=-z+4

-3z+z=4-1.5

-2z=2.5

z=-1.25 Or z= -
`(5)/(4)`

Substituting z value in equation (6)

3x=-(-1.25) +4

3x=5.25

x= 1.75

Or x=
`(7)/(4)`

Substituting z value in equation (2) and solving for y we have :

3y-2(-1.25)=7

or 3y=7-2.5

y=1.5

Or y=
`(3)/(2)`

The solutions to the equaitons are :

x=
`(7)/(4)`

y=
`(3)/(2)`

z=
`-(5)/(4)`