Solving Systems of Equations
When multiple variables have to be solved for, we have a system of equations.
In Algebra 1 class, we will look at 3 ways to solve systems of equations:
Solution by Graphing
Solution by Substitution
Solution by Elimination
Solution by Graphing:
Given the graphs of two equations, they are equal at their point of intersection, have no solution
if they are parallel, or have infinite solutions if they are multiples of each other.
Example y=2x. y=x2
Solution by Substitution:
Given two equations,
1)
2)
3)
4)
Express one variable in terms of the other
Let the expression for the variable replace it.
Solve for the value of the remaining variable
Find the value of the other variable
Solution by Elimination:
Given two equations
1) Combine equations so that one of the variables is eliminated
2) Solve for the value of the remaining variable
3) Find the value of the other variable