Checking solutions to linear systems

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean for an ordered pair to be a solution to a linear system?

Back

An ordered pair is a solution to a linear system if it satisfies all equations in the system.

Front

How do you check if an ordered pair is a solution to a linear system?

Back

Substitute the x and y values of the ordered pair into each equation of the system. If both equations are true, the pair is a solution.

Front

What is the graphical representation of a linear system?

Back

The graphical representation of a linear system is the intersection point(s) of the lines represented by the equations.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines in a linear system are parallel?

Back

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

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines in a linear system coincide?

Back

If two lines coincide, the system has infinitely many solutions because every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

What is the solution to the system of equations: y = 2x + 3 and y = -x + 1?

Back

The solution is (−2, −1).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables.

Tags

CCSS.8.EE.B.5

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution.

Tags

CCSS.8.EE.C.8B

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions.

Tags

CCSS.8.EE.C.8B