Answer
2; 0; (3, -1)
Work Step by Step
To break down elimination permanently, we must make the system of equations have no solutions. A way to do this is to make the first equation equal to the second equation by multiplication of a constant. If we make a=2, our system will be:
2x+3y=-3
4x+6y=6
Which can easily be seen as having no solutions after multiplying the first equation by 2. 4x+6y cannot equal 6 and -6 at the same time:
4x+6y=-6
4x+6y=6
To break down elimination temporarily, we must make the initial system impossible to eliminate while still having a solvable equation through other means (i.e. switching rows and back-substitution). If a=0, our new system of equations would be:
3y=-3
4x+6y=6
From this system, you cannot eliminate x from the second equation since there is no x variable in the first equation. You must solve the equation through other means. If we switch the position of the two equations, we will have a triangular system of equations and it will be possible to solve for x and y using back substitution.
4x+6y=6
3y=-3
3y=-3
y=-1
Substituting y=-1 into 4x+6y=6:
4x+6(-1)=6
4x-6=6
4x=12
x=3
(3, -1)
