Final: Where They Meet

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 59 of 61.

Both equations are already solved for y, so set their right-hand sides equal and solve for x. Substitute to find y. Substitution or elimination can also give the same solution.

Challenge

Hard

Solve the system $y = 3x+1;\quad y = -x-7$ .

Try it yourself

y = 3x+1

y = -x-7

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 Unknowns Two Numbers, Two Facts Recap: Two Methods

3Slope

Steepness as a Number Slope From Two Points Downhill Lines Flat and Straight Up A Fraction of a Slope Recap: Slope

6Standard Form

Ax + By = C The Two Intercepts Draw by Intercepts Between the Forms Recap: Standard Form

9Shaded Regions

A Line Splits the Plane Solid or Dashed Test a Point Rearrange, Then Shade Recap: Half-Planes Two Shadings Overlap The Corner of a Region

12Final Challenges

Final: Round TripFinal: Where They MeetFinal: Draw the Fence Final: The Whole Plane