Graphing Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The two lines represented by the equations intersect at exactly one point.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The two lines are parallel and never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

The two lines are the same line, meaning they overlap completely.

Tags

CCSS.8.EE.C.8A

Front

How can you graph a system of equations?

Back

By plotting each equation on the same coordinate plane and identifying points of intersection.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

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 'b' in the equation y = mx + b?

Back

'b' represents the y-intercept of the line.

Front

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

Back

(1, 3) is the solution where the two lines intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6