Solve by Graphing
In the form y=mx+b, what do the m and b represent?
slope and y-intercept
Solve the following system of equations by substitution:
y=x+1
y=2
(1,2)
Solve the following system of equations by elimination
x+y=10
x-y=2
(6,4)
What is the equation for slope?
rise over run
y2 - y1/ x2 - x1
If both equations in a system have the same slope and y-intercept, how many solutions exist to the equations?
infinite
Put the equation 5x = -y +3 into the form y=mx+b
y=-5x+3
The price of admission to FunPark is $10. Each ride costs $5 dollars. Write an equation to model the amount of money you would spend at FunPark.
c=5r+10
Each time Riley went to the school cafeteria, he bought either a cookie for $1.75 or pizza for $4.75. During the school year, he spent $490 and bought 160 food items. How many times did he by pizza?
Give the system of linear equations only.
490 = 1.75c + 4.75p
160 = c + p
Do parallel lines ever touch?
no
If a system of equations intersect, how many solutions does it have?
one
Solve the system of equations by graphing: y=5 and y=x+1. (sketch the graph)
(4,5)
Solve the following system of equations by substitution:
y=x+1
2x+y=7
(2,3)
Solve the system of equations by elimination:
4x-3y=-2
4x+5y=14
(1,2)
What are the equations for slope-intercept form and general form?
y= mx + b and Ax + By +C = 0
If a system of equations has no solution, what do you know about the graphs of the lines?
they are parallel
Solve the system of equations by graphing:
y=2x
2x=-y+12.
(3,6)
Solve the system of equations by substitution: 4x=8y
2x+5y=27
(6,3)
Solve each system of linear equations by elimination: 3x-y=17
y+2x=8
(5,-2)
If we have two lines that are perpendicular, what do we know about their slopes?
They are opposite reciprocals of each other
If the equations in a system have the same slope, but different y-intercepts, how many solutions does it have?
none
Solve the system of equations by graphing:
-x-2=-2y
2x-4y-4=0
no solution
Suppose you bought eight oranges and one grapefruit for a total of $4.60. Later that day, you bought six oranges and three grapefruits for a total of $4.80. Now you want to find the price of each orange and of each grapefruit. Write an equation for each purchase. Solve the system of equations.
8x+1g=4.60
6x+3g=4.80
each orange 50 cents, each grapefruit is 60 cents
A student can make a weekly salary of $200 plus 15% commission on sales at the Radio Barn or a weekly salary of $300 plus 10% on sales at Woofer, Etc. For what amount of sales do these two jobs pay the same? Write two equations and solve using elimination
y=0.15x+200
y=0.10x+300
20 sales per week
Write two equations.
1. Parallel to y= 5
2. Perpendicular to your first equation.
Answers will vary but should be y = constant and x = constant
Solve the following system of linear equations by substitution or elimination:
y= 4x + 4
-2x= -0.5y + 4
no solution