Two Numbers, Two Facts

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 57 of 64.

Word problems with two unknowns are systems in disguise: each fact becomes an equation. "Two numbers sum to 12 and differ by 4" says

x + y = 12

x - y = 4

Adding eliminates y: 2x = 16, so x = 8, and the sum then gives y = 4. Check against the story: 8 + 4 = 12, 8 - 4 = 4.

The translation habit from the earlier sections carries over whole: name the unknowns, write one equation per fact, and the system machinery does the rest.

Challenge

Two numbers sum to 15 and differ by 3. The facts written as equations are x + y = 15; x - y = 3. Solve the system for x and y.

Try it yourself

x + y = 15x - y = 3

Solve for x,y

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Graphs & Systems

1The Coordinate Plane

Two Numbers, One Point The Four Quadrants Points on the Axes Mirror Points Recap: The Plane

4Slope-Intercept Form

y = mx + b The Starting Height Write the Equation Solve for y Draw From Any Form Recap: y = mx + b

7Parallel & Perpendicular

Same Slope, Never Meet The Perpendicular Slope A Right-Angle Line Recap: Two Relations

10Systems by Graphing

Two Lines, One Answer Solve by Drawing Check the Crossing When Lines Never Cross Recap: By Graphing

2From Rule to Line

A Rule Makes Points The Points Line Up On the Line or Not?Between the Dots Recap: Rule to Line

5Point-Slope Form

A Point and a Slope From Two Points Flat or Vertical Through Draw From a Point Recap: Point-Slope

8Function Notation

The Name of a Rule Inputs With Signs Find the Input The Graph of f Recap: f(x)

11Solving Systems Exactly

Substitution Isolate First Elimination Scale, Then Add Three UnknownsTwo Numbers, Two FactsRecap: Two Methods