notes/education/math/Systems of Equations.md

Term	Definition
Consistent	The system of equations has at least one solution
Inconsistent	Parallel lines, no solution
Independent	The lines only cross at one point.
Dependant	The lines are identical, and there are infinitely many solutions. Both equations represent the same line when plotted.

Solving

Graphing

Graph the two equations, and look for points where they intersect

Substitution

Solve for a variable in the equation, then substitute it into another equation. EG, given the below systems:

 y = x+3 

 x = 3y + 2 

You can substitute values, like this:

 x = 3(x+3) + 2 

Then once you have x, you can plug it back into the first equation to solve for y.

Elimination

To solve a system of equations by elimination, you add the two equations together and see if something cancels out. A simple example might look like this:

 2x + 3y = 23 

 4x -3y = -13 

You "add" the two equations together, getting:

 6x + 0y = 10 

You now know that 6x = 10. If you don't have two values that evenly cancel out, like 3 and -4, you can find the least common multiple and multiply the entire equation so that those two are equal. In this case, you'd multiply one equation by 4, and one equation by 3. If the signs don't cancel out, you can multiply one of the equations by -1.