Algebraic Properties
If a=b, then a+c=b+c
What is the Addition Property of Equality?
Graphically and Algebraically
What are two ways to solve a system of equations?
y=mx+b
What is slope-intercept form?
> or < graphed with this type of line because the number is not part of the solution.
What is a dashed line?
The point where the lines intersect?
What is the solution to a system of intersecting lines?
If a=b, then a-c=b-c
What is the subtraction Property of Equality?
System of equations that has at least one solution. For example, a pair of intersecting lines or same lines
What is a consistent system?
What is the graphical solution to a system of linear equations?
>= or <= graphed with this type of line because the number is part of the solution.
What is a solid line?
ALL the points that lie within the shared overlapping shaded region of both inequalities.
What is the solutions to a system of inequalities?
If a=b, then a x c=b x c
What is the Multiplication Property of Equality?
System of equations that has no solution. For example, parallel lines
What is an inconsistent system?
Isolating one variable in an equation and substituting it into another.
What is substitution method?
Shade this area for > or >=
What is above the line?
Restrictions placed on a variable dependent on real-world situations.
What are constraints?
If a=b, then a/c=b/c
What is the Division Property of Equality?
When all of the solutions on one line are the same as the other line in a system. For example, the same line
What is a dependent system?
Eliminating one of the variables when combining two equations.
What is elimination method?
Shade this area for < or <=
What is below the line?
No possible value for x that would make the equation or inequality true.
What is No Solultion?
If a=b, then b can replace a in any expression without changing the value of the expression
What is the Substitution Property of Equality?
When 2 lines do not share all of the same points. For example, parallel lines or intersecting lines
What is an independent system?
Produced when any algebraic property is applied to either or both equations in a system and have the same solutions as the original system.
What is equivalent systems?
The line in the graph that divides the plane into two parts- one side represents points that are solutions and one side represents points that are not solutions.
What are boundary lines?
The equations describe the same line or the inequality has the same border line.
What is Infinitely Many Solutions?