Algebra 1: Solve Systems Using Elimination

Study Notes

Solving Systems of Equations Using Elimination

Elimination method involves manipulating equations to eliminate one variable, making it easier to solve for the other.

Example Problems and Solutions

Coordinates for (2):
- System: 3x + y = 5 and x - 2y = 4
- Solution: x-coordinate is 2.
Coordinates for (4):
- System: -3x + 2y = 5 and x - y = -3
- Solution: y-coordinate is 4.
Coordinates for (-5):
- System: 4x - y = 9 and x - 3y = 16
- Solution: y-coordinate is -5.
Coordinates for (7):
- System: x + 2y = 11 and x - y = 5
- Solution: x-coordinate is 7.

Types of Solutions

No Solution:
- Example: System of equations - 6x - 2y = 2 and 9x - 3y = 1 indicates parallel lines with no intersection.
Infinitely Many Solutions:
- Example: System 2x - 3y = 6 and -2x + 3y = -6 represents overlapping lines, thus infinitely many solutions.

Testing Solutions

Determine if specific points (x, y) are solutions to given systems.
Testing (-1, -2):
- System: x + 3y = -7 and 3x - 2y = 12
- Result: No, this point does not satisfy the system.
Testing (5, 2):
- System: x + y = 7 and 2x - 8 = y
- Result: Yes, this point meets both equations.

Solving by Elimination Method

Example with (3, 0):
- System: 2x + y = 6 and x - y = 3.
- Solution found using elimination is (3, 0).
Example with (6, 2):
- System: 5x - 3y = 24 and 3x + 5y = 28.
- Solution found via elimination is (6, 2).
Example with (-2, -9):
- System: x - 2y = 16 and -3x + y = -3.
- Solution using any method gives (-2, -9).
Example with (3, 1):
- System: 2x - 5y = 1 and 3x + 2y = 11.
- Using elimination method, the solution is (3, 1).

Description

This quiz challenges you to solve systems of equations using the elimination method. You will identify the x or y-coordinates of various equations. Test your algebra skills and deepen your understanding of systems of linear equations!