Unit One- Linear Systems

Unit One Key Concepts - to solve a system of two linear equations means to find the point of intersection of the two lines - check an answer by substituting it into the two original equations (equal answers means that it is right) - you can solve linear systems by graphing, using substitution, or elimination STEPS TO SOLVE BY SUBSTITUTION 1: Solve one of the equations for one variable in terms of the other variable. 2: Substitute the expression from step 1 into the other equation and solve for the remaining variable. 3: Substitute back into one of the original equations to find then value of the other variable. 4: Check the solution by substituting into both original equations. STEPS TO SOLVE BY ELIMINATION 1: Arrange equations so like terms are aligned. 2: Choose the variable you wish to eliminate. 3: If necessary, multiply one or both equations by a value so that they have the same or opposite coefficient in front of the variable you want to eliminate. 4: Add or subtract (as needed) to eliminate one variable. 5: Solve for the remaining variable. Substitute into one of the original equations to find the value fo the other variable. 6: Check solution by substituting into original equations. TYPES OF QUESTIONS Distance, Speed, Time A canoeist took 2 h to travel 12 km down a river. The return trip, against the current, took 3 h. What was the average paddling rate of the canoeist? What was the speed of the current? (pg 44) Direction Distance (km) Speed (km/h) Time (h) Downstream 12 P + c 2 Upstream 12 P – c 3   Mixture Problems Mariam has a bottle of 5% acetic acid and a bottle of 10% acetic acid. How much of each should she use to make 250 mL of 8% acetic acid? (pg 45) Volume (mL) 5% Acid 10% Acid 8% Mixture Solution F T 250 Pure Acid 0.05 f 0.1 t 0.08 (250)

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