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Vocabulary
Solve by Graphing
Substitution Method
Combination Method
Solutions
100
An ordered pair of numbers that is the solution to each equation in the system
What is a solution to a system of equations?
100
You can find the solution of two linear equations written in two variables by finding this point on the graph.
What is the point of intersection?
100
The answer to the system of 2x + y = 1 and 5x - 2y = -11.
What is (-1, 3)?
100
The combination method was used because I wanted this kind of answer.
What is an exact solution?
100
This system has no solutions.
What is an inconsistent system?
200
A method used to solve a system of equations in which variables are replaced with known values or algebraic expressions.
What is the substitution method?
200
The first step in solving a system of equations by graphing.
What is writing each equation in slope-intercept form?
200
The number of solutions to the system -x + y = 3 and x - y = -3
What is infinitely many solutions?
200
This property is used to get opposite coefficients for one of the variables.
What is the Multiplication Property of Equality?
200
This system may have one unique solution or infinitely many solutions.
What is a consistent system?
300
A method used to solve a system of equations in which you look for opposites of one of the variables.
What is the elimination or combination method.
300
These lines have the same slope.
What are parallel lines?
300
The answer to x + y = 2 and 1.5x - y = 3
What is (2, 0)?
300
This answer was found by using the combination method in solving 2x + 4y = 0 and 9x - 2y = -20.
What is (-2, 1)?
300
These lines show that there is one unique solution.
What are intersecting lines?
400
If a = b then a + c = b + c.
What is the Addition Property of Equality?
400
One of these lines has a slope that is the opposite of the reciprocal of the other.
What are perpendicular lines?
400
This is the solution to the system containing x + 2y = 4 and 3x + y = 7.
What is (10/7, 19/7)?
400
This related form to the Addition and Subtraction Properties of Equality is applied when we add the two equations in solving a system of equations by combination method.
What is If a = b and c = d, then a + c = b + d or if a = b and c = d, the a - c = b - d?
400
The equations 2x + 2y = 10 and 6x + 3y = -21 is this type of system.
What is a consistent system?
500
This kind of system has exactly one solution.
What is an independent consistent solution?
500
The system of 2x + y = 2 and 4x + 4y = 4 has this graph.
What are intersecting lines? (Student may say, "What has a solution of (1,0)?"
500
This is the description for solving a system of equations by substitution.
What is to first solve one of the equations for one of its variables. Then substitute the expression into the other equation and solve for the other variable. Lastly substitute the value found in the last step into one of the original equations or the revised equation from your first step and solve for the remaining variable.
500
These equations will show how many large size containers at $19.25 and how many small containers at $11.25 of Gatorade was bought for the March of Dimes Walk if exactly $1715 was spent and the shipment contained 62 containers.
What is L + S = 62 and $19.25L + $11.25S = $1715?
500
Both equations have the same slope-intercept form.
What equations have infinitely many solutions?