Question

Solve the following system of equations.

x + 4y + z = -10
3x - 3y + 6z = -21
x + 2y + 2z = -10

Can somebody do this out and show me how it's done? Thanks :]

Answer 1

sure...

Answer 2

I think that if you combine the equations in such a way as to eliminate variables, u can then solve for one of them. Then you can plug that number back in and solve for the rest!

Answer 3

u may apply elimination method

Answer 4

see, u hv three variables -- x, y and z and so three equations

x + 4y + z = -10 ----------------(1)
3x - 3y + 6z = -21 ----------------(2)
x + 2y + 2z = -10 ----------------(3)

We have to use these equations in pairs to eliminate two of the variables so that only one is left. This we do as follows:

First we take (1) and (2)
x + 4y + z = -10 ----------------(1)
3x - 3y + 6z = -21 ----------------(2)

Now multiply (1) by 3 to get equation (4) and subtract (2) from it
3x + 12y + 3z = -30 ----------------(4)
3x - 3y + 6z = -21 ----------------(2)
we get
15y - 3z = -9 ----------------(A)

Then we take (2) and (3)
3x - 3y + 6z = -21 ----------------(2)
x + 2y + 2z = -10 ----------------(3)

Now we multiply (3) by 3 to get eqn (5) and subtract it from (2)
3x - 3y + 6z = -21 ----------------(2)
3x + 6y + 6z = -30 ----------------(5)
we get
-9y = 9
y = 9/-9
y = -1

Answer 5

understood till this point.....????

Answer 6

Yep, I understand :]

Answer 7

Now substitute the y = -1 in equation (A)
15(-1) - 3z = -9
-15 -3z = -9
-3z = -9 + 15
z = 6/-3 =-2
z = -2

so till now we have y = -1 and z = -2

got it...????

Answer 8

Now substitute these values of y and z in (1)

x + 4y + z = -10
x + 4(-1) + (-2) = -10
x - 4 - 2 = -10
x = -10 + 6
x = -4

so solutions set (x,y,z) = (-4, -1, -2)

Answer 9

Thank you!

Answer 10

u r welcome.... ☺