MATHGOTSERVED Solving System of Equations
Learning Objective
On this page you will learn how to solve systems of two equations in two variables by:
1) Graphing
2) Linear Combination or Elimination
3) Substitution
Definition
A system of equation in two variables consists of two linear equations of the form

ax+by  c
dx+ey< f               dx+ey < f

The solution is the region that has the collection of ordered pairs (x,y) that satisfies both equations. The best  way to solve systems of linear inequalities is by graphing since the solution if it exists could be a line or region.

Solving Systems of two Linear Equations  by Graphing
How to Solve of Systems of Two Linear Inequalities by Graphing (Steps)
1. Graph the two inequalities (standard form: Ax+By=C), or the slope m, and intercept b (slope intercept form y=mx+b).
2. Find the feasible region of the two regions by using arrows.
3. The intersection of the feasible regions from the two graphs represents the solution to the system of linear inequalities.

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Interactive Practice
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