Graphing
Graph the equation y=-2x+1. What is the slope and y-intercept.
Y-intercept: (0, 1)
Solve the following system algebraically with substitution:
y=2x+1 and y=−x+7
(2,5)
Solve the following system algebraically with substitution:
3x−2y=11 and 5x+y=1
(1,-4)
Write a system of equations that has NO SOLUTION.
Any two equations where the slope is the same but the y-intercepts are NOT (parallel lines).
Ex: y=3x +1 and y=3x+2
A school is planning a field trip for 86 students. Each bus can hold 48 students. How many busses will the school need to rent?
2!
You can't rent part of a bus so we must round UP!
When the equations y=1/2x+2 and y=−1/2x+6 are graphed what is their solution (i.e. at what point do the lines intersect)?
(4,4)
Solve the following system algebraically with substitution:
y=−3x−2 and y=x−10
(2, -8)
Solve the following system algebraically with substitution:
1/2x+3/4y=4 and 2x−1/2y=2
(2,4)
How do we know when a system of equations has INFINITELY MANY SOLUTIONS?
The two equations have the same slope and y-intercepts and therefore are completely overlapping lines.
Ex: y=3x +1 and y=3x+1
Write an equation in slope-intercept form that appropriately represents the following scenario:
A gym charges a $25 registration fee plus $15 per month for membership.
y=15x+25
How many solutions does the system below have? Explain your reasoning.
y=3x−2 and y=3x+5
NONE (parallel)
Solve the following system algebraically with substitution:
y=1/2x+4 and 2x+y=−2
(-12/5, 14/5)
Solve the following system algebraically with substitution:
1/2x+y=3 and x+2y=8
Find the equation of a line that is perpendicular to a line that has an equation of y= -2x + 1 and passes through the point (2,2).
y=1/2x+1
The student council is selling tickets to a school dance. Online tickets cost a $3 service fee plus $7 per ticket. Tickets purchased at the door cost $12 per ticket, with no service fee.
Write (don't solve) a system of linear equations to represent this scenario. What does the variable x represent? What does the variable y represent?
y= 7x + 3 and y=12x
x = how many tickets purchased
y = total amount made by student council (tickets + service fees)
Solve the following system by graphing:
2x+3y=7 and 4x−2y=6
(2, 1)
Solve the following system algebraically with substitution:
y=−2x−1 and 3x+2y=0
(-2, 3)
Solve the following system algebraically with substitution:
2/3x−1/2y=4 and −4/3x+y=−8
A music streaming service charges a $6 monthly fee plus $0.50 for each song downloaded. Let x represent the number of songs downloaded and y represent the total monthly cost. Write a linear equation that represents the total cost based on the number of songs downloaded.
y= 1/2x+6 or y=0.5x+6
Two students are selling tickets for a school fundraiser. Maya has already sold 2 tickets and sells 2 more tickets each day. Carlos has already sold 4 tickets and sells 1 more ticket each day. How many days before they have sold the same amount of tickets?
Write two linear equations to represent the situation. Then graph both equations to determine the solution to the problem.
y=2x+2 and y=x+4
Solution: (2,6)
After 2 days, they've both sold 6 tickets.
Solve the following solution by graphing:
3x − 2y = 0
2x + 5y = -19
(-2, -3)
Solve the following system algebraically with substitution:
2x+3y=7 and 4x−y=−7
(-1,3)
Solve the following system algebraically with substitution:
−3x+1/2y=−10 and 5/2x−2y=2
(4,4)
Two friends are saving money for a concert. Ava starts with $25 and saves $10 each week. Liam starts with $55 and saves $5 each week. Let x represent the number of weeks and y represent the total amount of money saved.
1) Write a system of linear equations to represent the situation.
2) Decide whether you think the system would be easier to solve using the substitution method or the graphing method.
3) Solve the system and determine when Ava and Liam will have the same amount of money.
1) y=10x+25 and y=5x+55
2) Substitution
3) Solution: (6,85) (i.e. in 6 weeks they will both have $85)
Two students are saving money for a school trip. Alex starts with $43 and saves $12 per week. Jordan starts with $70 and saves $7 per week.
Write a system of two linear equations that represents the situation. Then determine how many WHOLE weeks it will take for Alex to have at least as much money as Jordan.
y= 12x+43 and y=7x+70
Solution: 5.4 weeks
6 WHOLE WEEKS