Intersection (Geometric) Math Example 1

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Example 1

easy
Find the intersection point of lines ℓ1:y=3x−2\ell_1: y = 3x - 2 and ℓ2:y=−x+6\ell_2: y = -x + 6.

Solution

  1. 1
    Step 1: Set equations equal (both equal yy): 3x−2=−x+63x - 2 = -x + 6.
  2. 2
    Step 2: Solve: 4x=8⇒x=24x = 8 \Rightarrow x = 2.
  3. 3
    Step 3: Substitute back: y=3(2)−2=4y = 3(2) - 2 = 4. Check: y=−(2)+6=4y = -(2) + 6 = 4. ✓

Answer

Intersection at (2,4)(2, 4).
Two non-parallel lines in a plane intersect at exactly one point, found by solving their equations simultaneously. Substituting back into both equations verifies the solution is correct.

About Intersection (Geometric)

The set of all points where two or more geometric objects (lines, planes, curves) meet or cross each other.

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More Intersection (Geometric) Examples

Example 2 medium

Find the intersection point(s) of line [formula] and circle [formula]. Classify the intersection (se

Example 3 easy

Do lines [formula] and [formula] intersect? Explain why or why not.

Example 4 hard

Find the intersection of the two circles: [formula] and [formula].

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Related Concepts

LineSystems of Equations