Systems of Two Equations

Overview

• The document is a worksheet titled "Systems of Two Equations" by Kuta Software LLC, focused on solving systems of equations using various methods.
• Published on July 26, 2012.

Methods to Solve Systems of Equations

1. Graphing

• Problem 1: Compare the lines:
  • Equations: (y = 3x + 4) and (y = 3x - 2)
  • Solution: (1, 1)
• Problem 2:
  • Equations: (y = x + 2) and (x = 3)
  • Solution: (3, 1)
• Problem 3:
  • Equations: (x - y = 3) and (7x - y = 3)
  • Solution: (1, 4)
• Problem 4:
  • Equations: (4x + y = 2) and (x - y = 3)
  • Solution: (1, 2)

2. Substitution

• Problem 5:
  • Equations: (y = 4x - 9) and (y = x - 3)
  • Solution: (2, 1)
• Problem 6:
  • Equations: (4x + 2y = 10) and (x - y = 13)
  • Solution: (6, 7)
• Problem 7:
  • Equations: (y = 5) and (5x + 4y = 20)
  • Solution: (0, 5)
• Problem 8:
  • Equations: (x + 7y = 0) and (2x - 8y = 22)
  • Solution: (7, 1)

3. Elimination

• Problem 15:
  • Equations: (8x - 6y = 20) and (16x + 7y = 30)
  • Solution: (1, 2)
• Problem 16:
  • Equations: (6x - 12y = 24) and (x - 6y = 4)
  • Solution: (2, 1)
• Problem 17:
  • Equations: (8x - 10y = 24) and (6x + 5y = 2)
  • Solution: (7, 8)
• Problem 18:
  • Equations: (24 - 8x = 12y) and (1 + 59y = 718x)
  • Solution: (6, 6)

Critical Thinking Questions

• Question 25: Write a system of equations with the solution (4, 3).
  • Example Solution: (x + y = 1), (2x + y = 5)

Additional Information

• The worksheet was created using Kuta Software’s Infinite Algebra 2 tool.
• Free trials for creating similar worksheets are available at KutaSoftware.com.