Question

solve each system
2x-y+z =7
y+z =5

Answer 1

Is this linear algebra?

Answer 2

system of equations and inequalities

Answer 3

Do you know what a matrix is?

Answer 4

havt gotten there yet

Answer 5

Your system of equations in this case is not complete. You have 3 variables but only 2 equations.

Answer 6

This means you need to have a free variable.

Answer 7

Are you familiar with this concept?

Answer 8

that is the question to be answered
and i think adding those two will also eliminate y from the equation

Answer 9

i was supposed to be a three variable then u add the first two to get a different equation and u add the first and third to get another equation then u solve for variables

Answer 10

not three variable but three equations

Answer 11

You can't create a third equation from the existing equations, because that would be redundant.

Answer 12

It's like saying: \[
x+y=2\\
2x+2y=4
\]They're not independent equations, so they might as well be only a single equation.

Answer 13

In any case, add the equations together to get: \[
2x+2z=12 \implies x=6-z
\]

Answer 14

Next, subtract \(z\) from both sides of the second equation: \[
y=5-z
\]

Answer 15

Our solution to the system will be \((x,y,z) = (6-z,5-z,z)\).
We need the free variable \(z\) because we just don't have enough equations to solve for it.