INTRO Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of 2 or more equations that have the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The lines representing 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

The lines representing the equations coincide, meaning they are the same line.

Tags

CCSS.8.EE.C.8A

Front

How can you determine the number of solutions in a system of equations?

Back

By graphing the equations and observing the intersection points.

Tags

CCSS.8.EE.C.8B

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the graphical representation of a system of linear equations?

Back

It is represented by lines on a coordinate plane.

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

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

Back

The slope indicates the steepness and direction of the line.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear equation?

Back

The y-coordinate where the line crosses the y-axis.