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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.

Tags

CCSS.8.EE.C.8B

Front

What does it mean for a system of equations to have one solution?

Back

A system has one solution when the graphs of the equations intersect at exactly one point, indicating a unique solution for the variables.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have no solution?

Back

A system has no solution when the graphs of the equations are parallel and never intersect, indicating that there are no values for the variables that satisfy all equations.

Tags

CCSS.8.EE.C.8A

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

A system has infinitely many solutions when the equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

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

Back

To determine the solution graphically, plot the equations on a coordinate plane and identify the point(s) where the graphs intersect.

Tags

CCSS.8.EE.C.8B

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the coordinates (-4, -2) in a system of equations?

Back

The coordinates (-4, -2) represent a specific point on the graph where the two equations intersect, indicating the solution to the system.

Tags

CCSS.8.EE.C.8A

Front

How can you verify if a point is a solution to a system of equations?

Back

To verify if a point is a solution, substitute the coordinates of the point into both equations. If both equations are satisfied, the point is a solution.

Front

What is the role of the slope in determining the relationship between two lines in a system of equations?

Back

The slope indicates the steepness and direction of a line. If two lines have the same slope but different y-intercepts, they are parallel and have no solution.

Tags

CCSS.8.EE.C.8B