Algebra 1: Systems of Equations Quiz

Solutions to Systems of Equations

• The point (4, -4) is the solution to a specific system of equations.
• The point (-1, -1) serves as another solution for a different system.

Types of Solutions

• No Solution: Occurs when two equations represent parallel lines, exemplified by the equations -2x + y = 5 and -2x + y = -7.
• Infinite Solutions: Indicates that the equations represent the same line. For instance, 8x + 2y = 4 and 4x + y = 2 yield infinite solutions.

Methods of Solving Systems

• Substitution Method: The solution (2, 1) is found using the equations y = 6x - 11 and -2x - 3y = -7.
• Graphing Method: The point (2, 3) is obtained by graphing the equations y = 5x - 7 and -3x - 2y = -12.
• Elimination Method: The solution (6, -6) arises from the equations -4x - 2y = -12 and 4x + 8y = -24.

Specific Solutions

• The point (10, -1) is found by applying the substitution method on the equations x = y + 11 and 2x + y = 19.
• The point (-1, -8) is identified using substitution with the equations 8x + y = -16 and -3x + y = -5.
• The solution (-6, 0) is obtained using any method applied to the equations 5x + 4y = -30 and 3x - 9y = -18.

Values of Coordinates

• For the system defined by x + 2y = 9 and x - y = 3, the value of the y-coordinate of the solution is 2.
• For the system defined by x - 2y = 1 and x + 4y = 7, the value of the y-coordinate of the solution is 1.