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 to the system is the set of values that satisfy all equations simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

A point is a solution to a system of equations if, when the coordinates of the point are substituted into each equation, they satisfy all equations in the system.

Front

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

Back

To determine if a point is a solution, substitute the x and y coordinates of the point into each equation. If the equations hold true, the point is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the intersection of the lines represented by each equation. The intersection point(s) represent the solution(s) to the system.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if a system of equations has no solution?

Back

A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if a system of equations has infinitely many solutions?

Back

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

Tags

CCSS.8.EE.C.8A

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the values of the variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the elimination method for 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 coefficients in a system of equations?

Back

The coefficients in a system of equations determine the slope and position of the lines represented by the equations, affecting the number of solutions.

Tags

CCSS.8.EE.C.8B

Front

How do you identify a consistent system of equations?

Back

A consistent system of equations has at least one solution, which can be either a single point of intersection or infinitely many solutions.

Tags

CCSS.8.EE.C.8B