Algebra 1 Unit 6 Review Flashcards

Questions and Answers

What is a system of equations?

A collection of 1 or more equations

A collection of 2 or more equations joined by the AND truth condition (correct)

An equation with a single variable

None of the above

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?

Find the intersection of the 2 graphs.

What is the first step in solving a system of equations algebraically with the substitution method?

Solve one of the equations for either x or y. Signup and view all the answers

What is the purpose of multiplying both sides of an equation in the elimination method?

To eliminate (create a zero) a variable. Signup and view all the answers

Equals may always substitute for ____________.

equals Signup and view all the answers

What does the Multiplication Property of Equality state?

You can multiply or divide by the same quantity on both sides of an equation and retain the equality. Signup and view all the answers

How do you solve a system of inequalities graphically?

Find the intersection of the 2 shaded regions of the inequalities. Signup and view all the answers

What is defined as a point (x, y) that makes all inequalities true?

Solutions to a System of Inequalities Signup and view all the answers

What is the Slope-Intercept Form of a Line?

Not provided Signup and view all the answers

What does 'linSolve' refer to?

Solving system of equations on the TI-nSpire. Signup and view all the answers

How do you find intersection points on the TI-nSpire?

Graph page: menu 8, 1, 3, click on both graphs. Signup and view all the answers

How do you graph an inequality on the TI-nSpire?

Graph page: delete the = in the equation box. Signup and view all the answers

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.

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.