Solve systems of two linear equations exactly and approximately using algebraic and graphical methods.
Build and solve a system for a break-even context
Problem
Plan A costs \(\$20\) plus \(\$5~\text{per}~\text{month}\), and Plan B costs \(\$8\) plus \(\$8~\text{per}~\text{month}\). Write both linear models and solve for the point where their costs are equal.
Big Picture
What this problem is really about
Each plan needs a total-cost model built from its fixed fee and its rate per month. We’ll use the same input and output variables for both plans, place fixed amounts as constants and rates as coefficients, and set the totals equal at break-even. Substitution into both models verifies the shared cost, and the ordered pair must be interpreted with months first and dollars second.
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