Intermediate Algebra
Linear Systems
Two conditions at once: find the point that keeps both, by graph and by algebra, then shade where inequalities agree.
THE SYLLABUS
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Two Constraints
One purchase gives two facts: how many things were bought and what they cost. Written with unknown counts, each fact becomes an equation, and together they make a system.
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Graph of a System
Every point on a graph of counts is one purchase: its coordinates are the counts. Points on the line x + y = 12 all hold 12 pieces, but each one costs a different amount.
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Solution to a System
Many purchases share a count and many share a cost, but only one keeps both: the solution to the system, where the two lines cross.
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Graphing Constraints
Each constraint is a line: rule it through two of its points, such as where it meets the axes. Graph both constraints and the solution is where the lines cross, even when that is on an axis.
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Building a System
Write each constraint as an equation yourself: the count, then the cost. Graph both, and the crossing gives the solution to the system.
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Level Check
Fifteen questions across Level 1: write the constraints, graph them, and read the solution.
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II
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III
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IV
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V
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VI
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