Algebra 1: Solve Systems Using Elimination

What is the x-coordinate of the solution for the system 3x + y = 5 and x - 2y = 4?

What is the y-coordinate of the solution for the system -3x + 2y = 5 and x - y = -3?

What is the y-coordinate of the solution for the system 4x - y = 9 and x - 3y = 16?

What is the x-coordinate of the solution for the system x + 2y = 11 and x - y = 5?

What is the outcome of the system 6x - 2y = 2 and 9x - 3y = 1?

What is the outcome of the system 2x - 3y = 6 and -2x + 3y = -6?

Is (-1, -2) a solution to the system x + 3y = -7 and 3x - 2y = 12?

Is (5, 2) a solution to the system x + y = 7 and 2x - 8 = y?

What is the solution to the system 2x + y = 6 and x - y = 3?

What is the solution to the system 5x - 3y = 24 and 3x + 5y = 28?

What is the solution to the system x - 2y = 16 and -3x + y = -3?

What is the solution to the system 2x - 5y = 1 and 3x + 2y = 11?

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).

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!