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.
Answer 11 questions on Algebraic Techniques for Equations.
1. What is algebraic substitution?
2. In the example y = 2x + 3, if x = 4, what is the value of y after substitution?
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