GED® Algebra: Systems of Equations & Linear Modeling Mastery
A focused GED® Mathematical Reasoning algebra course on systems of equations, graphical intersections, checking ordered-pair solutions, substitution, elimination, no-solution and infinitely-many-solution cases, and real-world linear modeling. Students learn to compare plans, write break-even equations, translate ticket and number problems, and choose a reliable solving strategy.
📚 Course Curriculum
A system of equations is a set of equations that must be true at the same time. In algebra, a system usually asks for the …
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Graphically, each line shows all ordered pairs that make its equation true. The intersection point lies on both lines, so it satisfies both equations. If …
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An ordered pair solves a system only if it makes both equations true. Example: Check whether \((2,3)\) solves:. First equation:. is true. Second equation:. is …
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Substitution is often best when one equation already has a variable isolated, such as \(y=x+1\) or \(x=2y\). [[figure:systems_substitution_flow Substitution replaces one variable with an equivalent …
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Elimination is often best when adding or subtracting the equations can cancel one variable. [[figure:systems_elimination_balance Elimination adds or subtracts equations so one variable disappears.]]. Example:. …
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Some systems do not have exactly one intersection. If two lines have the same slope but different y-intercepts, they are parallel:. They never meet, so …
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A word problem becomes a system when two conditions must be true at the same time. Example: Adult tickets cost 12 dollars, child tickets cost …
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A linear model often has the form:. Here \(m\) is the rate of change and \(b\) is the starting value. Example: A rental company charges …
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A break-even point is where two costs, earnings, or quantities are equal. [[figure:break_even_model_graph The break-even point is where the two linear models have the same …
Open trial session →Many GED® systems use a total count and a total value. Ticket example:. The first equation counts tickets. The second equation counts dollars. Number example: …
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A system may appear as a table, graph, or verbal description rather than two equations. From a table, create a linear model by finding the …
Open trial session →Choose the method that matches the structure. Use graphing when the intersection is easy to read and exact enough. Use substitution when a variable is …
Open trial session →Course Syllabus
Course Outcomes
📝 Practice Questions
50 interactive questions with instant feedback and explanations.
Enroll for free to unlock the full practice bank after the trial sessions.