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?
- A set of two or more equations with the same variables
- What is a solution to a system of two linear equations?
- The point (x, y) where both equations are true simultaneously
- What does the solution to a system represent graphically?
- The point where the two lines intersect
- What does it mean if a system of equations has no solution?
- The lines are parallel and never intersect
- What does it mean if a system of equations has infinitely many solutions?
- The two equations represent the same line
- What is the substitution method for solving systems?
- Solving one equation for a variable and substituting it into the other equation
- What is the elimination (addition) method for solving systems?
- Adding or subtracting equations to eliminate one variable
- Solve by substitution: y = x + 2 and y = 3x
- x = 1, y = 3
- What is the first step in solving a system by elimination?
- Aligning the equations and, if needed, multiplying to make coefficients match
- What is a consistent system of equations?
- A system that has at least one solution
- What is an inconsistent system of equations?
- A system that has no solution
- What is a dependent system of equations?
- A system with infinitely many solutions (the same line)
- What is an independent system of equations?
- A system with exactly one solution
- How can you solve a system of equations graphically?
- Graph both equations and find their point of intersection
- What is a system of linear inequalities?
- Two or more linear inequalities considered together
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