Parallel/Perpendicular Lines & Model Systems
Solving Systems
Graphing Systems of Equations & Inequalities
Solve/Graph Absolute Value Equations
100
Are the following lines parallel, perpendicular, or neither? Explain your choice.
y = 2x + 4
3x + 6y = 7
Perpendicular
The slopes are m = 2 and m = -1/2 , which are negative reciprocals of each other.
100
Solve the system with substitution
y = 3x + 6
y = 4x - 4
(10 , 36)
100
Graph the system and state the solution:
y=-1/2x-2
y=-3/2x+2
(4 , -4)
100
Solve for x
-3|x+2| + 8 = 8
x = -2
200
Write the equation of the line in slope-intercept form that is parallel to the line 3y + 12x = -5 and passes through the point (-8,7).
y = -4x - 25
200
Solve the system with elimination
5x - 3y = 10
5x - y = 12
(13/5 , 1)
200
Graph the systems of equations and state the solution.
y = 4x - 5
-8x + 2y = 10
No Solution
200
Solve for x
-5|x+7| = 35
No Solution
300
The sum of two numbers is 27. The sum of 3 times the first number and 2 times the second number is 67. What are the two numbers?
First number is 13 and the second number is 14.
300
Solve the system with substitution
x + 7y = 0
2x - 8y = 22
(7 , -1)
300
Is the point (-4,1) a solution to the following systems of inequalities?
-2x + 5y ≥ 10
y < -.5x - 3
NO, it works for the first equation, but not the second equation.
300
Write the equation for the following graph:
y=1/2|x-4|
400
Write the equation of the line in standard form that is perpendicular to the line 3y + 12x = -5 and passes through the point (-8,7).
x - 4y = -36
400
Solve the system with elimination
2x - 6y = 9
-6x + 18y = -27
Infinite Solutions
400
Graph the following systems of inequalities:
y<3
y≥-3/2x-2
400
Graph the following equation. Graph at least 7 points.
y = -|x+3| + 4
500
Suppose you have a store that sells long-sleeve shirts and short-sleeve shirts. Long-sleeve shirts cost $42.19 and short-sleeve shirts cost $32.84. On one day, you sold a total of 80 shirts and made $3029.25. How many of each kind of shirt did you sell? (Use a calculator)
You sold 43 long sleeve shirts and 37 short-sleeve shirts.
500
Solve the system with elimination
−8x − 10y = 24
6x + 5y = 2
(7 , -8)
500
Sarah is selling bracelets and earrings to make money for summer vacation. The bracelets cost $2 and the earrings cost $3. She needs to make at least $60. Sarah knows she will sell more than 10 bracelets and earrings total. Write inequalities and graph to represent the income from jewelry sold and number of bracelets sold.
x + y > 10
2x + 3y ≥ 60
500
Solve for x
6 + 2|x - 5| = 24
x = -4 and x = 14