Systems of Equations Graphs

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system of equations has at least one solution, meaning the graphs of the equations intersect at one or more points.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system of equations has no solutions, meaning the graphs of the equations do not intersect at any point.

Front

What is the graphical representation of a linear equation?

Back

The graphical representation of a linear equation is a straight line on a coordinate plane.

Front

How can you determine the solution of a system of equations graphically?

Back

The solution of a system of equations can be determined graphically by finding the point(s) where the graphs of the equations intersect.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts, indicating that the system of equations is inconsistent.

Front

What is the point of intersection in a system of equations?

Back

The point of intersection is the solution to the system of equations, representing the values of the variables that satisfy all equations in the system.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.