Systems
Riddle: My two lines cross at exactly one point, giving a single ordered pair as the answer. What am I?
Definition: A system that has exactly one solution.
independent system
Riddle: I solve systems by adding or subtracting equations so that one variable disappears. What method am I?
Definition: Using addition or subtraction to eliminate a variable in a system of equations.
elimination method
Riddle: I am a coordinate that makes a single inequality true when you substitute the values. What am I?
Definition: An ordered pair that makes an inequality true.
solution of an inequality
Riddle: My lines never meet, no matter how far they extend. Because of this, there is no ordered pair that works for both equations. What am I?
Definition: A system that has no solution.
inconsistent system
Riddle: First solve one equation for a variable, then place that expression into the other equation to find the solution. What method am I?
Definition: Solving a system of equations by solving one equation and substituting the result into the other equation.
substitution method
Riddle: I am a coordinate that lies in the overlapping shaded region when multiple inequalities are graphed. What am I?
Definition: An ordered pair that makes all the inequalities in a system true.
solution of a system of linear inequalities
Riddle: I am a group of inequalities working together instead of equations. Each one compares values using <, >, ≤, or ≥. What am I?
Definition: Two or more linear inequalities considered together.
system of linear inequalities
Riddle: I look like an equation, but instead of an equal sign I compare values using symbols like greater than or less than. An example is y > x − 5. What am I?
Definition: An inequality that compares two linear expressions, such as y > x − 5.
linear inequality
Riddle: I’m a pair of numbers that satisfies every equation in a system at the same time, such as (0, 3). What am I?
Definition: An ordered pair that makes all of the equations in a system true.
solution of a system of linear equations
Riddle: I bring together two or more linear equations to be solved at the same time, like y = 3x + 2 and y = −5x − 3. What am I?
Definition: Two or more linear equations considered together.
system of linear equations
Riddle: My equations always work out somehow. Maybe the lines cross once or overlap forever, but there is always at least one solution. What am I?
Definition: A system of equations that is either independent or dependent because it has at least one solution.
consistent system
Riddle: I’m a pair of equations that overlap perfectly. Every point on the line works for both of us, giving more answers than you can count. What am I?
Definition: A system that has infinitely many solutions.
dependent system