Question

solve the following systems of equations
2x-y-z=-3
2x+2y+3z=2
3x-3y-z=-4

Answer 1

first set the equations = to 0

Answer 2

Which equation? I learned like using elimination method or substitution method and im just confused.

Answer 3

ok which do you want to use?

Answer 4

we can use the first one @Austin6i6

Answer 5

a system of equation is nothing more complicated than a "n" number of equations with "n" number of variables.
And our objetive when solving one, are the variables that solves all the equations at the simultaneusly.
So, let's call the equations 1 , 2 and 3:
\[1) 2x-y-z=-3\]
\[2) 2x+2y+3z=2\]
\[3)3x-3y-z=-4\]
So, our objective is ti reduce the number of variables and create two other equations with two variables, and make it a 2x2 system of equations.
In order to do that, we will take equation 1), multiply it by -1 and add it to the equation 2):
\[1)-2x+y+z=3\]
\[2)2x+2y+3z=2\]
So adding them up, we will create equation 4):
\[4) 3y+4z=5\]
And we will do it analogically for another pair.But this time, we have to eliminate the same variable we used to create equation 4):
Si I will take equation 1) and multiply it by -3 and equation 3) and multiply it by 2:
\[1)-6x+3y+3z=18\]
\[3)6x-6y-2z=-8\]
Now, we will sum them so we can create equation 5):
\[5)3y+z=10\]
Now that we have made two equations, with only ttwo variables, all you have to do is solve a 2x2 system. Consisting of:
\[4) 3y+4z=5\]
\[5)3y+z=10\]

Answer 6

Do you know anything about matrics

Answer 7

hwo did you get 18? I thought 3 times 3 is 9?

Answer 8

oops, I thought of it as 6, it's 9 yes.

Answer 9

so the sum woudl acutally be -3y-5z=1?

Answer 10

brijackson6 do you know anything about matrics?

Answer 11

no i dont sorry

Answer 12

ok, because if you did it would make this problem so simple. nvm stick to whats here.