ACT Math

A comprehensive course covering the essential math concepts and strategies needed to excel on the ACT.

Advanced Topics

Systems of Equations and Inequalities

Combining Multiple Equations

Systems involve solving for values that satisfy more than one equation at the same time.

Types

  • Systems of Equations: Two or more equations, solved together
  • Inequalities: Using \( <, >, \leq, \geq \) instead of \( = \)

Solving Systems

  • Substitution: Replace one variable with an equivalent expression
  • Elimination: Add/subtract equations to eliminate a variable

Graphing

  • The solution is where the equations' graphs intersect

Real-World Scenarios

Systems help with comparing phone plans, budgeting, or scheduling.

ACT Advice

Check if you can add or subtract equations to make solving easier.

Examples

  • Solving: \( x + y = 10 \), \( x - y = 2 \) — Add: \( 2x = 12 \Rightarrow x = 6, y = 4 \)

  • Graphing \( y > 2x - 1 \) means shading above the line \( y = 2x - 1 \)

In a Nutshell

Systems of equations help solve real problems by combining multiple constraints.