8.1 Systems of Equations in Two Variables Day 1 Do Now Solve for y 1) X – y = 5 2) 2x + y = 1.

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Presentation transcript:

8.1 Systems of Equations in Two Variables Day 1 Do Now Solve for y 1) X – y = 5 2) 2x + y = 1

System of Equations There are three ways to solve a system of equations in two variables: – Graphing – Substitution – Elimination

Solving by Graphing When graphing a system of equations, the solution is the intersection – 1 solution: 1 intersection – 0 solutions: parallel lines – Infinitely many solutions: lines are identical

Ex Solve by graphing

Substitution Method 1) Solve equation 1 for one variable 2) Substitute equation 1 into equation 2 3) Solve for remaining variable 4) Solve for 2 nd variable

Ex Solve using substitution

Elimination Method 1) Multiply both equations by constants so that one pair of variables have the same coefficient 2) Add or subtract equations to eliminate 1 variable 3) Solve for the remaining variable 4) Solve for the 2 nd variable

Ex Solve using the elimination method

Ex Solve

Ex Solve

Ex Solve

Closure Solve HW: p.688 #1-37 odds

8.1 Systems of Equations in Two Variables Day 2 Do Now Solve

HW Review: p.688 #1-37 odds

Applications When approaching a word problem, and there are 2 different measurements, you want to write one equation for each measurement

Ex At SnackMix.com, caramel corn worth $2.50 per pound is mixed with honey roasted mixed nuts worth $7.50 per pound in order to be 20 lbs of a mixture worth $4.50 per pound. How much of each snack is used?

Ex Kerry’s motorboat takes 3 hr to make a downstream trip with a 3mph current. The return trip against the same current takes 5 hr. Find the speed of the boat in still water

Ex The price and supply of a satellite radio are related by the equation y = x The price and demand of the radio are related by the equation y = 200 – 25x The equilibrium point for this product is when both are equal. Find the equilibrium point

Closure College students spend a total of $819 on textbooks and computer equipment. They spend $183 more on textbooks than on computer equipment. How much do they spend on each one? HW: p.689 #41-61 odds

8.1 Systems of Equations Day 3 Do Now Jackson Manufacturing offers its sales reps a choice between being paid a commission of 8% sales or being paid a monthly salary of $1500 plus a commission of 1% of sales. For what monthly sales do the two plans pay the same amount?

HW Review: p.689 #41-61

Closure How do you solve a system of equations in 2 variables? Which method do you prefer? Why? HW: none