Algebra 1 Unit 6 Review Flashcards

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.