Graphing Systems

Learn and apply graphing systems using equations, examples, and interpretation.

Lesson 1 of 53 parts Practice Flashcards

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Intersection as Solution

Objective: Explain and use intersection as solution in an Algebra 1 problem.

A solution to two equations in x and y is an ordered pair satisfying both; on graphs it appears at their intersection. A point on only one line is not a system solution.

Worked examples

Try itExample 1.1: The lines y=x+14 and y=−x+24 intersect at what x-coordinate?Show answer

5. Set the two expressions for y equal and solve for x. The answer is 5.

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Intersection as Solution

Objective: Explain and use intersection as solution in an Algebra 1 problem.

A solution to two equations in x and y is an ordered pair satisfying both; on graphs it appears at their intersection. A point on only one line is not a system solution.

Worked examples

Try itExample 1.1: The lines y=x+14 and y=−x+24 intersect at what x-coordinate?Show answer

5. Set the two expressions for y equal and solve for x. The answer is 5.

One Intersection

Objective: Explain and use one intersection in an Algebra 1 problem.

Two nonparallel lines meet exactly once, giving one ordered-pair solution. Different slopes.

Worked examples

Try itExample 2.1: The lines y=x+24 and y=−x+40 intersect at what x-coordinate?Show answer

8. Set the two expressions for y equal and solve for x. The answer is 8.

Graph Precision

Objective: Explain and use graph precision in an Algebra 1 problem.

A graph may suggest a solution but a coordinate estimated from a drawing should be checked algebraically for exactness. Drawing scale and thickness can hide exact values.

Worked examples

Try itExample 3.1: The lines y=x+34 and y=−x+56 intersect at what x-coordinate?Show answer

11. Set the two expressions for y equal and solve for x. The answer is 11.

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