Finding the Number of Solutions to Linear Equations: Using Tables and Graphs

This lesson teaches how to determine the number of solutions to a pair of linear equations using tables and graphs. It covers three examples: Amanda and Beatrice's parallel lines with no solution, Catlin and Devon's identical lines with infinitely many solutions, and Eric and Fran's intersecting lines with one solution. The lesson concludes by summarizing the conditions for no solution, one solution, and infinitely many solutions in linear systems.

What is a solution to a pair of linear equations?

• A pair of values that satisfies both equations

• A single value that satisfies one equation

• A point that lies on the x-axis

• A point that lies on the y-axis

Why do Amanda and Beatrice never have the same amount of money?

• Because their lines are parallel

• Because their savings rates are different

• Because Beatrice starts with more money

• Because Amanda saves more money each week

What does it mean if two lines on a graph are parallel?

• They never intersect

• They are the same line

• They intersect at one point

• They intersect at multiple points

How often do Catlin and Devon have the same amount of money?

• Once

• Never

• Twice

• Infinitely many times

What indicates that there are infinitely many solutions to a system of equations?

• The lines coincide

• The lines are parallel

• The lines intersect at one point

• The lines are perpendicular

When do Eric and Fran have the same amount of money?

• After 6 weeks

• Never

• After 4 weeks

• After 2 weeks

What conclusion can be drawn if two lines intersect at one point?

• There is one solution

• There are infinitely many solutions

• The lines are parallel

• There is no solution