Algebra 1, Unit 4: Systems of Equations. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
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- What is a system of equations?
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A set of two or more equations with the same variables- What is a solution to a system of two linear equations?
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The point (x, y) where both equations are true simultaneously- What does the solution to a system represent graphically?
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The point where the two lines intersect- What does it mean if a system of equations has no solution?
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The lines are parallel and never intersect- What does it mean if a system of equations has infinitely many solutions?
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The two equations represent the same line- What is the substitution method for solving systems?
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Solving one equation for a variable and substituting it into the other equation- What is the elimination (addition) method for solving systems?
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Adding or subtracting equations to eliminate one variable- Solve by substitution: y = x + 2 and y = 3x
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x = 1, y = 3- What is the first step in solving a system by elimination?
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Aligning the equations and, if needed, multiplying to make coefficients match- What is a consistent system of equations?
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A system that has at least one solution- What is an inconsistent system of equations?
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A system that has no solution- What is a dependent system of equations?
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A system with infinitely many solutions (the same line)- What is an independent system of equations?
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A system with exactly one solution- How can you solve a system of equations graphically?
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Graph both equations and find their point of intersection- What is a system of linear inequalities?
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Two or more linear inequalities considered together
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