SECONDARY ONE 6.1b Solving Linear Systems by Graphing.

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Presentation transcript:

SECONDARY ONE 6.1b Solving Linear Systems by Graphing

SYSTEM OF LINEAR EQUATIONS Two or more linear equations in the same variable. Example: 2x + 4y = 12 -4x + 3y = 6

SOLUTION OF A SYSTEM OF LINEAR EQUATIONS An ordered pair (x, y) that satisfy each equation in the system.

3 WAYS TO SOLVE A SYSTEM OF LINEAR EQUATIONS 1. Graphing – Find where the two lines cross 2. Substitution – solve one equation for one variable and plug it into the other equation. 3. Elimination (linear combination) – add the equations together.

SOLVE A SYSTEM BY GRAPHING Step 1: Write each equation in a form that is easy to graph. Step 2: Graph both equations on the same coordinate plane Step 3: Estimate where the two lines cross. Step 4: Check by plugging back into equations.

SOLVE BY GRAPHING

2x + y = 5 -2x – y = -1

SOLVE BY GRAPHING y = 2x x + 2y = 6

WRITE A SYSTEM OF LINEAR EQUATIONS TO REPRESENT EACH PROBLEM SITUATION. DEFINE EACH VARIABLE. THEN, GRAPH THE SYSTEM OF EQUATIONS AND ESTIMATE THE BREAK-EVEN POINT. EXPLAIN WHAT THE BREAK-EVEN POINT REPRESENTS WITH RESPECT TO THE GIVEN PROBLEM SITUATION. Eric sells model cars from a booth at a local flea market. He purchases each model car from a distributor for $12, and the flea market charges him a booth fee of $50. Eric sells each model car for $20.

ERIC SELLS MODEL CARS FROM A BOOTH AT A LOCAL FLEA MARKET. HE PURCHASES EACH MODEL CAR FROM A DISTRIBUTOR FOR $12, AND THE FLEA MARKET CHARGES HIM A BOOTH FEE OF $50. ERIC SELLS EACH MODEL CAR FOR $20. What if you wanted to find the exact break-even point?

BOTTOM OF PAGE 372

ASSIGNMENT 6.1 Assignment # 2