Graphing
y = x + 1
y = 2x - 1
(2,3)
y = 2x + 3
y = 3x + 5
(-2,-1)
x + 4y = 4
-x + 2y = 8
(-4,2)
A beach shop sells umbrellas for $16 each and chairs for $10 each. The shop sells a total of 28 items today and earned $400. Write and solve a system of equations to find the number of umbrellas and the number of chairs sold.
20 umbrellas
8 chairs
Find the slope of a line that goes through the following two points
(-4,6) (10, 12)
3/7
y = -x - 2
y = 1/4x + 3
(-4,2)
2x + y = 4
-3x + y = -1
(1,2)
9x + y = 2
3x + y = -4
(1,-7)
At a sporting event, the price for 3 pretzels and 2 cups of soda is $14. The price for 2 pretzels and 4 cups of soda is $12. Write and solve a system of equations to find the price of each pretzel and each water.
$4 pretzels and $1 water
Graph a line that is proportional (direct variation)
It must be straight and touch the origin
y = -x - 1
2y = -2x - 2
many solutions
y = 3x + 4
x + y = 8
(1,7)
x + 6y = 12
x+ 3y = 3
(-6,3)
At a restaurant, you eat 2 tacos and drink 2 glasses of ice tea for a cost of $13. Your friend eats one taco and drinks 3 glasses of ice tea for a cost of $11.50. Write and solve a system of equations to find the cost of a taco and the cost of a glass of ice tea.
$4 taco and $2.50 Ice tea
A(-3,6)
Find A' after a reflection over the y-axis.
A'= (3,6)
-x + 2y = 2
-3x + 4y = 8
(-4,-1)
-2x + 3y = 9
y = 2x + 7
(-3,1)
2x + 10y = -20
-x + 4y = 28
(-20,2)
The math club has 40 members. The number of girls is 2 times the number of boys minus 5. Write and solve a system of equations to find the number of girls and the number of boys.
15 boys and 25 girls
What is the sum of the degrees of the interior angles of a 12-gon?
1800 degrees
Explain how to tell if the system of equations will have no solution BEFORE graphing
It will have the same slope and a different y-intercept
Which equation would you re-arrange. EXPLAIN WHY
-2x + 4y = 7
3x + y = -11
3x - y = -11 because the y has a coefficient of 1
If you want to eliminate the y value, which equation do you need to change and what do you multiply by?
-6x + 3y = 14
5x + 15y = 10
The top equation would be multiplied by -5
THere are a total of 27 red and blue marbles in a bag. Three times the number of blue is equal to five more than the number of red marbles. Write and solve a system of equations to find the number of blue marbles and the number of red marbles.
8 blue marbles and 19 red marbles.
Write the following equation in standard form
-3x + 4y - 6 = 0
3x - 4y = -6