Flashcards: Algebraic Techniques for Equations — 22 cards

Algebraic substitution — definition?

Replacing variables with known values or expressions.

Substitution steps — first step?

Write the original expression or equation.

Literal equations — role?

Rearranged to solve for any variable.

Rearranging formulas — mechanism?

Use inverse operations to isolate a variable.

Restrictions on variables — purpose?

Identify values that make expressions undefined.

Linear functions — form?

Expressed as y = mx + c.

Graphing lines — key point?

Plot y-intercept and use slope for slope-intercept form.

Solving simultaneous equations — method?

Find the point(s) satisfying all equations.

Graphical methods — advantage?

Visualize solutions as intersections of lines.

Substitution method — process?

Solve one equation for a variable, then substitute.

Elimination method — process?

Add or subtract equations to cancel a variable.

Linear equation — what?

Equation representing a straight line.

Gradient — symbol?

m in y = mx + c.

Y-intercept — meaning?

Point where line crosses y-axis.

Graphing lines — key step?

Plot intercepts or use slope and points.

Simultaneous equations — solution?

Values satisfying all equations simultaneously.

Substitution method — best when?

One equation easily solved for a variable.

Elimination method — best when?

Coefficients of a variable are opposites or can be made so.

Graphical methods — main idea?

Find intersections of lines to solve systems.

Restrictions on variables — how found?

Set denominators to zero or radicands < 0.

Linear functions — key feature?

Constant rate of change, straight line graph.

Graphing lines — essential?

Determine slope and intercepts for accurate plotting.