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Questions and Answers
What is a system of equations?
What is a system of equations?
What is defined as a point (x, y) that makes all equations true in a system?
What is defined as a point (x, y) that makes all equations true in a system?
Solutions to a System of Equations
How do you solve a system of equations graphically?
How do you solve a system of equations graphically?
Find the intersection of the 2 graphs.
What is the first step in solving a system of equations algebraically with the substitution method?
What is the first step in solving a system of equations algebraically with the substitution method?
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What is the purpose of multiplying both sides of an equation in the elimination method?
What is the purpose of multiplying both sides of an equation in the elimination method?
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Equals may always substitute for ____________.
Equals may always substitute for ____________.
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What does the Multiplication Property of Equality state?
What does the Multiplication Property of Equality state?
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How do you solve a system of inequalities graphically?
How do you solve a system of inequalities graphically?
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What is defined as a point (x, y) that makes all inequalities true?
What is defined as a point (x, y) that makes all inequalities true?
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What is the Slope-Intercept Form of a Line?
What is the Slope-Intercept Form of a Line?
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What does 'linSolve' refer to?
What does 'linSolve' refer to?
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How do you find intersection points on the TI-nSpire?
How do you find intersection points on the TI-nSpire?
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How do you graph an inequality on the TI-nSpire?
How do you graph an inequality on the TI-nSpire?
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Study Notes
System of Equations
- Comprises 2 or more equations linked by the AND truth condition.
Solutions to a System of Equations
- Represented as a point (x, y) that satisfies all equations in the system.
Solving a System of Equations Graphically
- Involves finding the intersection point of the two graphs, where both equations are true for x and y.
Substitution Method
- Solve one equation for x or y, if not already isolated.
- Substitute the derived value into the other equation to find the remaining variable.
Elimination Method
- Select a multiple to eliminate a variable when equations are added.
- Apply the Multiplication Property of Equality to modify one or both equations, creating a new system conducive to eliminating a variable.
Equals Substitution
- Equals can always be substituted for equals, maintaining the integrity of equations.
Multiplication Property of Equality
- Allows multiplication or division of both sides of an equation by the same non-zero quantity without altering the equality.
Solving a System of Inequalities Graphically
- Requires finding the intersection of the two shaded regions represented by the inequalities.
Solutions to a System of Inequalities
- Identified by a point (x, y) that satisfies all inequalities, lying within the overlapping shaded area.
Slope-Intercept Form of a Line
- Generally expressed as y = mx + b, where m is the slope and b is the y-intercept.
linSolve on TI-nSpire
- Access via menu: 3, then select 2 for solving systems of equations using the TI-nSpire calculator.
Finding Intersection Points on TI-nSpire
- Use the graph page: navigate to menu 8, then select 1 and 3 after clicking on both graphs.
Graphing an Inequality on TI-nSpire
- In the equation box, remove the equality sign (=) to properly graph the inequality.
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Description
Test your knowledge of systems of equations with these flashcards. This quiz focuses on key definitions and concepts related to solving equations graphically and algebraically. Perfect for reviewing algebraic principles before exams.
