Solving Simultaneous Equations Using Elimination Method

Introduction to Simultaneous Equations

• Simultaneous equations are pairs of equations that need to be solved together by finding a set of x and y values that satisfy both equations.
• The elimination method involves combining the two equations to eliminate one variable.

Basic Steps in the Elimination Method

1. Label Equations: Label the equations as 1 and 2 for reference.
2. Eliminate One Variable:
   • Combine the equations to cancel out one variable (either x or y).
3. Solve for Remaining Variable:
   • Solve the resulting equation for the remaining variable.
4. Substitute Back:
   • Substitute the found variable back into one of the original equations to find the other variable.
5. Double Check:
   • Verify the solution by plugging the values back into the other original equation.

Example 1: Basic Problem

• Equations:
  • 1: 7x + 2y = 23
  • 2: 3x + 2y = 11

Steps

• Subtract equation 2 from equation 1:
  • Result: 4x = 12
  • Solve for x: x = 3
• Substitute x = 3 back into equation 1:
  • Solve for y: y = 1
• Solution: x = 3, y = 1
• Verification: Plug into equation 2 to ensure it works.

Example 2: More Complex Problem

• Equations:
  • 1: 4x + y = 10
  • 2: 3y = 2x - 19

Steps

• Rearrange Equation 2 into standard form:
  • New form: -2x + 3y = -19
• Equalize x coefficients by multiplying equation 2 by -2:
  • Result: 4x - 6y = 38
• Subtract equation 1 from new equation 2:
  • Result: 7y = -28
  • Solve for y: y = -4
• Substitute y = -4 back into equation 1:
  • Solve for x: x = 3.5
• Solution: x = 3.5, y = -4
• Verification: Plug into rearranged equation 2 to ensure it works.

Additional Information

• Amadeus mentions a learning platform offering free resources for sciences and maths.
• Links to more content and resources for further practice are available on their platform.