Lecture on Solving Simultaneous Equations Using Elimination Method

Introduction to Simultaneous Equations

• Pairs of equations that need to be solved together.
• Solutions are pairs of x and y values that satisfy both equations.

Elimination Method Overview

• Aim: Combine two equations to eliminate one variable.
• Process reduces the system to a single equation with one unknown.

Step-by-Step Example 1

1. Label Equations: Label the given equations as 1 and 2.
2. Combine Equations:
   • Subtract one equation from the other to eliminate variables.
   • Example: Eliminate y by doing (Equation 1 - Equation 2).
3. Simplify:
   • 7x - 3x = 4x
   • 2y - 2y = 0
   • 23 - 11 = 12
4. Solve for x:
   • 4x = 12
   • x = 3 (after dividing both sides by 4)
5. Substitute back to find y:
   • Substitute x = 3 into any original equation.
   • Example: 7(3) + 2y = 23 → 2y = 2 → y = 1.
6. Verify Solutions:
   • Substitute x = 3 and y = 1 into the other equation to verify.

Step-by-Step Example 2

1. Label and Arrange:
   • Label equations as 1 and 2.
   • Arrange both equations in the form: ax + by = c.
   • Example: Adjust Equation 2 by subtracting 2x from both sides to get -2x + 3y = -19.
2. Equalize Coefficients:
   • Equalize x or y coefficients by multiplying equations.
   • Example: Multiply Equation 2 by -2 to match x-coefficients.
3. Eliminate Variable:
   • Subtract Equation 2 from Equation 1 to eliminate x.
   • Resulting equation: 7y = -28.
4. Solve for y:
   • y = -4 (after dividing by 7).
5. Substitute back to find x:
   • Use y = -4 in original Equation 1.
   • Example: 4x - 4 = 10 → 4x = 14 → x = 3.5.
6. Verify Solutions:
   • Plug x = 3.5 and y = -4 into the other equation for verification.

Conclusion

• Double-check solutions by substituting back into both original equations.
• Confidence in solutions is increased through verification.

Additional Resources

• Mention of learning platform with videos, practice questions, and progress tracking.
• Links provided for further learning and organized playlists.

Final Note

• Encouragement to explore the learning platform for more resources and practice.