Question

Solve the system of equations.

Answer 1

C.
`(x=8,y=-5,z=0)`

Explanation:

We have been given a system of equations and we are asked to solve our given system of equations.

`3x+4y+4z=4...(1)`

`5x+7y+3z=5...(2)`

`4x+5y+7z=7...(3)`

Using equation (1) and equation (2) we will eliminate z.

`3*3x+4*3y+4*3z=4*3...(1)`

`5*4x+7*4y+3*4z=5*4...(2)`

`9x+12y+12z=12...(1)`

`20x+28y+12z=20...(2)`

Subtracting equation (1) from equation (2) we will get,

`11x+16y=8...(4)`

Similarly we will eliminate z using equation (2) and (3).

`5*7x+7*7y+3*7z=5*7...(2)`

`4*3x+5*3y+7*3z=7*3...(3)`

`35x+49y+21z=35...(2)`

`12x+15y+21z=21...(3)`

Subtracting equation (3) from equation (2) we will get,

`23x+34y=14...(5)`

Now we will use substitution method to solve equation (4) and (5).

From equation (4) we will get,

`x=(8-16y)/(11)`

Substituting this value in equation (5) we will get,

`23((8-16y)/(11))+34y=14`

`(184-368y)/(11)+34y=14`

Let us have a common denominator.

`(184-368y)/(11)+(34*11y)/(11)=14`

`(184-368y)/(11)+(374y)/(11)=14`

`(184-368y+374y)/(11)=14`

`(184+6y)/(11)=14`

`(184+6y)/(11)*11=14*11`

`184+6y=154`

`184-184+6y=154-184`

`6y=-30`

`(6y)/(6)=(-30)/(6)`

`y=-5`

Therefore, y equals negative 5.

Substituting
`y=-5` in equation (4) we will get,

`11x+16(-5)=8`

`11x-80=8`

`11x-80+80=8+80`

`11x=88`

`(11x)/(11)=(88)/(11)`

`x=8`

Therefore, x equals 8.

Substituting
`y=-5` and
`x=8` in equation (1) we will get,

`3*8+4(-5)+4z=4`

`24-20+4z=4`

`4+4z=4`

`4-4+4z=4-4`

`4z=0`

`z=0`

Therefore, the value of z is 0.

Upon looking at our given choices we can see that option C is the correct choice.