Presentation on theme: "3.1 Solving Systems by Graphing or Substitution"— Presentation transcript:
1 3.1 Solving Systems by Graphing or Substitution Learning Objective: to solve systems using both methodsWarm-up (IN)1. Write each equation in slope intercept form.y=x-9y=2/5xy=-4/7x+2y=15x-30y=3x-3.24
2 NotesLinear System –a set of 2 or more equations in 2 or more variablesSolution –An ordered pair, (x, y), that satisfies all of the equationsCoincidingparallelintersectingInfinitely many solutionsno solutionsOne solution
3 Consistent System –Has at least one solutionIndependent System –Exactly one solutionDependent System –Infinitely many solutionsInconsistent System –no solutions***To solve by graphing1 – Graph both lines2 – Estimate point where they intersect3 – Check by plugging the point into the 2 equations
4 EX 1 – solve by graphing and classify the system Consistent and independent(-1, 3)yesyes
5 ***To solve systems by substitution: 1 – get one variable by itself in one equation2 – Substitute that expression into the other equation3 – Solve for the variable4 – plug that value back into either of the original equations to find the other variable
6 EX 2 – Solve by substitution: Always write solution as an ordered pair!!!