SOLUTION: x+y-2z=0 3x+y=1 5x+3y+7z=2 x= y= z=

Question 253952: x+y-2z=0
3x+y=1
5x+3y+7z=2
x=
y=
z=
Found 3 solutions by jim_thompson5910, dabanfield, drk:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the second equation.

Subtract 3x from both sides.

Move back to the first equation

Plug in

Combine like terms.

Subtract 1 from both sides.

Multiply every term by -1

So let's make equation 4

Move onto the third equation

Plug in

Distribute

Combine like terms.

Subtract 3 from both sides.

Combine like terms. We'll make this equation 5.

--------------------------------------------------------------------------

So we have the new system of equations:

Multiply the both sides of the first equation by 2.

Distribute and multiply.

So we now have

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Divide both sides by to isolate .

------------------------------------------------------------------

Now go back to the first equation.

Plug in .

Multiply.

Multiply both sides by the LCD to clear any fractions.

Distribute and multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

Go back to the previously isolated equation.

Plug in

Combine like terms.

So the solutions are , and .

Which form the ordered triple .

This means that the system is consistent and independent.
Answer by dabanfield(803)   (Show Source): You can put this solution on YOUR website!
1)x+y-2z=0
2)3x+y=1
3)5x+3y+7z=2
From equation 1 we have y=2z-x
So if (from equation 2) 3x+y = 1 then
3x+(2z-x)= 1
3x+2z-x = 1
and
From equation 3:
5x+3*(2z-x) + 7z = 2
Solve these two equations for x an z then substitute in the first equation to find y.

Answer by drk(1908)   (Show Source): You can put this solution on YOUR website!
We have three equations:
(i)
(ii)
(iii)
solve (ii) for y. We get
(iv)
substitute (iv) into (i) and (iii) to get 2 equations with two variables.
(v)
(vi)
simplify (v) and (vi) to get
(vii)
multiply (vii) by -2 to get
(ix)
(viii)
add down to eliminate x and solve for z. We get
(x) 11z = 1 - -> z = 1/11.
Find x.
x = 9/11
Find y.
y = -16/22
So, we have
{9/22 , -5/22 , 1/11}
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