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System Solution Types and Applications

Algebra Foundation

Algebra 1

Study expressions, equations, inequalities, functions, linear models, systems, polynomials, quadratics, and exponential growth with original explanations and worked examples.

Learn with original explanations and worked examples. OpenStax Elementary Algebra 2e was consulted for topic coverage.

Study every current unit through original concept lessons, formula derivations, experiments, quizzes, and practice sets.

Algebra 1 · Unit 6 · Topic 6.4

System Solution Types and Applications

Two lines may intersect once, be distinct and parallel, or coincide.

Definition and explanation

Two lines may intersect once, be distinct and parallel, or coincide. These cases correspond to one solution, no solution, or infinitely many solutions; application answers must also meet the context's restrictions.

Worked example

There are 12 tickets costing either $6 or $9, and total revenue is $90. With a low-price tickets and b high-price tickets, a + b = 12 and 6a + 9b = 90. Subtract 6(a + b) = 72 to get 3b = 18, so b = 6 and a = 6.

Common mistake

Fractional ticket counts are not valid even if an unrestricted algebraic system produces them.

Key takeaway

Two lines may intersect once, be distinct and parallel, or coincide.

Explain each step of the worked example, then check the units, signs, and conditions that apply.

Further reading

Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.