3.1 – Solve Linear Systems by Graphing A system of two linear equations in two variables x and y, also called a linear system, consists of two equations that can be written in the following form. Ax + By = C Dx + Ey = F A solution of a system of linear equations in two variables is an ordered pair that satisfies each equation.

3.1 – Solve Linear Systems by Graphing Example 4: Graph the linear system and estimate the solution. Then check the solution algebraically. 3x + 2y = -4 x + 3y = 1

3.1 – Solve Linear Systems by Graphing Example 5: Graph the linear system and estimate the solution. Then check the solution algebraically. 4x – 5y = -10 2x – 7y = 4

3.1 – Solve Linear Systems by Graphing A system that has at least one solution is consistent. If a system has no solution, the system is inconsistent. A consistent system that has exactly one solution is independent and a consistent system that has infinitely many solutions is dependent.

3.1 – Solve Linear Systems by Graphing

Example 6: Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. 4x – 3y = 8 8x – 8y = 16

3.1 – Solve Linear Systems by Graphing Example 7: Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. 2x + y = 4 2x + y = 1