Using algebra to find the point of intersection of two lines

Find the exact point of intersection of two given straight lines algebraically, and verify that the coordinate satisfies both equations.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA6-5
New NZC (2026)
  • NZC26-P4-ALG-ER-P-Y10-02

Resources

Terminology

  • point of intersection
  • simultaneous equations
  • equate
  • substitute
  • eliminate
  • ordered pair
  • verify

Task goals

  • Foundation: Equate two y = mx + c rules, solve for x, substitute to find y, and write the exact intersection coordinate.
  • Proficient: Rearrange a mixed-form pair or eliminate a variable, including negative and fractional values, then verify the solution in both equations.
  • Excellence: Select an efficient algebraic route for two given linear relationships and justify the exact common point, including a tightly framed comparison context.

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Using algebra to find the point of intersection of two lines

Using algebra to find the point of intersection of two lines

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Forming and solving linear equations and linear inequalities with rational number coefficients (e.g. −2/5 x + 5 ≤ −10), giving exact or rounded solutions, and representing the solution on a number line

Statement▸
Year 10 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-P-Y10-02

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