Graphing
Where does the two lines intersect?
x + 2
-x + 4
Point (1,3)
Solve the system of linear equations by substitution.
y = 2x+ 3
y = 5x
(1,5)
x = 1
y = 5
3x + 4y = -6
7x + 4y = -14
(-2,0)
Solve the system of linear equations.
x = 2y + 10
2x + 3y = -1
(4,-3)
Solve for c
19 - 4c = 17
c = 0.5
What are the y-intercepts and point of intersection?
3x - 3
2x
y-intercepts: (0,0) (0,-3)
point of intersection: (3,6)
Solve the system of linear equations by substitution.
4x + 2y = 0
y = -0.5x - 5
(2,-4)
2x + 5y = 16
3x - 5y = -1
(3,2)
y = 1/3 x + 1
-x + 3y = -6
no solution
Solve for x
1.1x + 1.2x - 5.4 = -10
x = -2
What are the y-intercepts and point of intersection?
2x + 4
6x - 7
y-intercepts: (0,4) (0,-7)
point of intersection: (2.75,9.5)
Solve using substitution.
y = 2x + 5
y = 3x - 1
(6,17)
4x - 5y = -19
-x - 2y = 8
(-6,-1)
y = - 1/6 x + 5
x + 6y = 30
infinitely many solutions; all points on the line
y = - 1/6 x + 5
Write in slope-intercept form an equation for the line that passes through the given points.
(-9,5), (-3,3)
y = -1/3 x + 2
Give the equations for the lines on the graph.
y=-4x-7
x+y=2 or y=-x+2
An animal shelter has a total of 65 abandoned cats and dogs. The ratio of cats to dogs is 6:7. How many cats are in the shelter? How many dogs are in the shelter?
30 cats, 35 dogs
5x = 4y + 8
3y = 3x - 3
(4,3)
-2x + y = 1.3
2(0.5x - y) = 4.6
(-2.4,-3.5)
y = -140x + 500
Write an equation that represents the costs. Write an equation that represents the revenue. Find where the two lines intersect.
Your family starts a bed and breakfast. it spends $500 fixing up a bedroom to rent. the cost for food and utilities is $10 per night. Your family charges $60 per night to rent the bedroom.
Cost: y=10x+500
Revenue: y=60x
point of intersection: (10,600)
Write a system of linear equations.
What is the cost of each ticket?
x = 2y
64x + 132y = 1040
adult = $8
student = $4
You can jog around your block twice and the park once in 10 minutes. You can jog around your block twice and the park 3 times in 22 minutes.
Write a system of linear equations.
How long does it take to jog around the park?
2x + y = 10
2x + 3y = 22
It takes 6 minutes.
You downloaded a digital album for $10. Then you and your friend downloaded the same number of individual songs for $0.99 each.
Write a system of equations for the situation.
Will you and your friend spend the same amount of money?
y = 0.99x + 10
y = 0.99x
no because you paid $10 before buying the same number of songs at the same price, you spend $10 more
If there were ten fish in an enclosed tank, and four swam away, three died, and three drowned, how many fish would be left?
Seven fish, fish can't drown and can't swim away in a tank