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solve the system of equations
x+y-z=2
-x+2y-3z=-7
x+5y-3z=21
~~~~~~~~~~~~~~~~~~
x + y - z = 2, (1)
-x + 2y - 3z = -7, (2)
x + 5y - 3z = 21. (3)
There are different methods to solve it.
I will use the Elimination method here.
Add the equations (1) and (2). You will get
3y - 4z = -5. (4)
Add the equations (2) and (3). You will get
7y - 6z = 14. (5)
Thus you excluded (eliminated) "x" from the system (1), (2), (3) and got the system (4) and (5) of TWO equations in TWO unknowns.
Since you just study on how to solve 3x3 equations, I suppose that solving the 2x2 system (4), (5) is not a big problem to you.
You can apply the Elimination method one more time to the system (4), (5).
On solving systems of linear equations in two unknowns see the lessons
- Solution of the linear system of two equations in two unknowns by the Substitution method
- Solution of the linear system of two equations in two unknowns using determinant
- Solution of the linear system of two equations in two unknowns by the Elimination method
- Geometric interpretation of the linear system of two equations in two unknowns
- Solving word problems using linear systems of two equations in two unknowns
On solving systems of linear equations in three unknowns see the lessons
- Solving systems of linear equations in 3 unknowns by the Substitution method
- BRIEFLY on solving systems of linear equations in 3 unknowns by the Substitution method
- Solving systems of linear equations in 3 unknowns by the Elimination method
- BRIEFLY on solving systems of linear equations in 3 unknowns by the Elimination method