8.1 Systems of Equations in Two VariablesDay 1

Do NowSolve 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 2nd 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 2nd 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 VariablesDay 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 = 90 + 30x

• 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 EquationsDay 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