graphing and substitution systems

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

It means that the equations represent the same line, resulting in an infinite number of intersection points.

Tags

CCSS.8.EE.C.8A

Front

How can you determine if a system of equations has one solution, none, or infinitely many solutions?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Tags

CCSS.8.EE.C.8B

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of the lines of the equations plotted on a coordinate plane.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The point of intersection represents the solution to the system, where both equations are satisfied.

Tags

CCSS.8.EE.C.8B

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What does it mean if two lines are perpendicular in a system of equations?

Back

It means that the lines intersect at a right angle and will have one unique solution.

Tags

CCSS.8.EE.C.8B