8.1 systems of equations in two variables day 1 do now solve for y 1) x – y = 5 2) 2x + y = 1
TRANSCRIPT
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