Types
Common
knowledge
knowledge
Solve
Graphing
Slope
100
Describe the solution of a system of two linear equations that have the same slope and the same y-intercept.
Infinitely many solutions (Dependent Consistent System)
100
True or False:
It does not matter which method you use when solving systems of linear equations because they will all give you the same answer (when solved correctly).
True
100
Identify which method is commonly used for this system, then solve the system of linear equations:
Y = 2x + 9
Y= -x + 6
Graphing, (-1,7)
100
What is Graphing? Why do we draw lines and shaded regions for equations and inequalities.
A collection of points that satisfy an equation or inequality. We don't draw every point, but instead draw lines and shaded regions.
100
What is Slope?
Slope is a value that describes the "steepness" and direction of a line.
200
Describe the solution of a system of two linear equations that have different slopes and the same y-intercept.
One solution (Independent Consistent System)
200
How do we write solutions to systems of linear equations?
Coordinate form, (x,y) or individually (x = #, y = #)
200
Identify which method is commonly used for this system, then solve the system of linear equations:
y = 2x + 5
y = 1/2x - 1
(-4,-3)
200
What are linear equations?
Linear equations are an algebraic equation of the form y = mx+b
200
What is a Y intercept?
The y-intercept is the point (coordinate) where the graph intersects the y-axis.
300
Describe the solution of a system of two linear equations that have the same slope and different y-intercepts.
No solution (Inconsistent System)
300
How many linear equations will be in a system of linear equations?
At least 2 linear equations
300
Identify which method is commonly used for this system, then solve the system of linear equations:
2x = y - 10
x + 7 = y
(-3,4)
300
What is the solution to the system of linear equations?
(2,2)
300
What makes a slope undefined?
A vertical line. An infinite rise divided by a zero run.
400
The system of linear equations is given below, what is the solution set?
y = 2x + 3
2y = 4x + 6
Infinitely many solutions (Dependent Consistent System)
400
What does it mean to "find the solution" to a system of linear equations?
It means to find the point of intersection of a graph, or to find the (x,y) coordinate whose values satisfy all equations within the system.
400
Identify which method is commonly used for this system, then solve the system of linear equations:
x + 4y = 1
3x + 5y = 10
(5,-1)
400
What is the solution?
(-1,-1)
400
What are the three common linear equation formats?
Slope Intercept, Y = mx + b
Point Slope, y - y1 = m(x - x1)
Standard, Ax + By = C
500
The system of linear equations is given below, what is the solution set?
4x + 2y = 8
6x + 3y = 6
No solution (Inconsistent System)
500
Describe the numeric relationship between slopes of parallel lines and slopes of perpendicular lines.
Slopes of parallel lines are EQUAL
Slopes of perpendicular lines are OPPOSITE RECIPROCALS.
500
Identify which method is commonly used for this system, then solve the system of linear equations:
y = 5x - 9
y = 5x + 9
No solution.
500
How many solutions does the system of linear equations have?
One
500
Slopes of linear equations can be described as numerical values that are: positive, negative, _______________, and _______________. HINT: y = # and x = #.
Positive, Negative, Zero and Undefined.