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Multi-Step Linear Equations
Linear Equations and Number of Solutions
Systems of Equations
Slope-Intercept Form
Interpreting Slope
100
What is the solution to the following equation: 8x + 4 - 2x = 6 + 5x - 3?
What is x = -1.
100
How many solutions does the equation 2x + 4 = 2x + 4 have? A) No solutions B) 1, x = 2 C) 1, x = 4 D) Infinite Solutions
What is D) Infinite Solutions
100
When would a system of equations have no solution? Give an example.
A system of equations will have no solution when the lines have the same slope (they are parallel and therefore do not intersect). EG) y = 2x + 4 and y = 2x + 8
100
Find the slope of the line between the following points: (5, -2) and (-6, 7).
What is -9/11.
100
Which of these equations has the steepest slope: A) y = 6x + 1 B) y = -2x + 20 C) y = 1/2x + 7 D) y = 4x + 2
What is A) y = 6x + 1
200
On night 1, NJPAC sold 20 adult tickets and 5 children's tickets for a total of $225. A total of 15 people attended the event. Write a system of equations to represent the above situation. How much did it cost for an adult ticket? How much did it cost for a child's ticket?
What is $10 per adult ticket and $5 per child ticket.
200
How many solutions does the following system of equations have: 2y + 4x = 8 and y = 1/3(-6x + 24)?
What is no solution (The lines are parallel because they have the same slope --> y = -2x + 4 and y = -2x + 8).
200
Solve the following system of equations: 4x + 8y = 20 and -4x + 2y = -30.
What is (7, -1)
200
Find the equation of line whose slope is m = 2 and passes through the point (-1, 5).
What is y = 2x + 7.
200
Verizon charges a flat rate of $20 plus $40 an hour for a service call. If a customer paid $200 total, how many hours it total was the service call?
What is 4.5 hours.
300
Solve for the following: 1/6(2x + 4) = 2
What is x = 4.
300
What is the solution to the following equation: 4x + 3x + 14 = 2x + 7 + 5x?
What is no solution.
300
Solve the following system of equations by substitution: y = 6x - 11 and -2x - 3y = -7.
What is (2, 1).
300
Find the equation of the line that passes through the points (2, 4) and (-1, 1).
What is y = 1x + 2.
300
What is the slope of the following linear equation: y = 2? What type of line is it?
What is 0. The line is horizontal.
400
Solve the equation below for x: -1/3(x + 9) + x = 1.
What is 6.
400
Given the equation 2x - 4y = 12, give an other equation where there will be A) an infinite number of solutions, B) No solution, C) and 1 solution.
A) y = 1/2x -3 B) y = 1/2x + any number C) y = (any number except 1/2)x + any number
400
Solve the following system of equations: -3x - 8y = 20 and -5x + y = 19.
What is (-4, -1).
400
Write the following equation in slope-intercept form: 3x + 5y = -5
What is y = -3/5x -1
400
The slope of a line through the point (4, 8) is 3. Which point is also on the line? A) (7, 5) B) (1, 5) C) (2, 2) D) (-1, 4)
What is C) (2, 2)
500
Solve for the variable: −5(1 − 5x) + 5(−8x − 2) = −4x − 8x
What is -5.
500
Which statement above the following system of equations is true: 3x + 2y = -4 and 2x - 3y = 3: A) There is no solution. B) There is an infinite number of solutions. C) There is one solution, and the lines are not perpendicular. D) There is one solution, and the lines are perpendicular.
What is D) There is one solution, and the lines are perpendicular. (y = -3/2x -2 and y = 2/3x -1).
500
Given the following system of equations: x - y = 11 and 2x + y = 19. What is the value of x + 3y?
The solution is (10, -1). Therefore, x + 3y is 7.
500
Which equation represents a function with a rate of change that is greater than the rate of change of the line 6x – 2y = –14? A) y = 1/2x + 12 B) y = 2x + 4 C) y = 4x - 1 D) y = x + 20
What is y = 4x - 1 (the given equation converts to y = 3x + 7 and 4 >3).
500
The equation of a line is y = 3x + 5. As the value of x increases by 2, what happens to the value of y?
What is is increases by 6.