Two Numbers, Two Facts

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 59 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

Medium

Two numbers sum to 15 and differ by 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