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Two Numbers, Two Facts

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 56 of 61.

A word problem with two unknowns can be written as a system. Each fact in the problem becomes one equation. Take the problem "Two numbers sum to 12 and differ by 4". Call the numbers $x$ and $y$ . The two facts give:

$x+y = 12$

$x-y = 4$

Add the equations to eliminate $y$ : $2x = 16$ , so $x = 8$ . The first equation then gives $8+y = 12$ , so $y = 4$ . Check the answer against the problem: $8+4 = 12$ and $8-4 = 4$ .

Define the two unknowns and write an equation for each relationship in the problem. Then solve the equations together, using substitution or elimination.

Challenge

Medium

Two numbers sum to 15 and differ by 3. Solve the system for $x$ and $y$ .

Try it yourself

x+y = 15

x-y = 3

Find $x$ , $y$

All lessons in Graphs & Systems

1Points and Rules

Two Numbers, One Point A Rule Makes Points The Points Line Up

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

2The Whole Plane

The Four Quadrants Mirror Points On the Line or Not?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