Systems of Equations- Graphing & Word Problems

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 to graph a system of equations?

Back

It means to plot the equations on a coordinate plane to find their intersection point, which represents the solution.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Tags

CCSS.8.EE.C.8B

Front

How do you determine if a system of equations has no solution?

Back

If the lines are parallel and never intersect, the system has no solution.

Tags

CCSS.8.EE.C.8A

Front

What is the meaning of a consistent system of equations?

Back

A system that has at least one solution.

Tags

CCSS.8.EE.C.8B

Front

What is the meaning of an inconsistent system of equations?

Back

A system that has no solutions.

Tags

CCSS.8.EE.C.8A

Front

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

Back

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

How do you find the y-intercept of a linear equation?

Back

Set x = 0 in the equation and solve for y.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line; a positive slope rises, while a negative slope falls.

Tags

CCSS.8.EE.B.5

Front

How can you represent a word problem as a system of equations?

Back

Identify the variables, write equations based on the relationships described, and set them equal to each other.

Tags

CCSS.HSA.CED.A.3