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Systems of Equations Flashcards

6 cards from real Algebra Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 Systems of Equations flashcards as text

  1. Solve by elimination: 3x + 2y = 16 and x - 2y = 0

    Answer: x = 4, y = 2

    Adding the equations gives 4x = 16, so x = 4; substituting gives y = 2.

  2. Two linear equations with the same slope but different y-intercepts have:

    Answer: No solution

    Equal slopes with different y-intercepts mean the lines are parallel with no intersection.

  3. Solve: y = 3x - 1 and y = x + 5

    Answer: x = 3, y = 8

    Set 3x - 1 = x + 5, so 2x = 6 and x = 3; then y = 8.

  4. What is the solution to: x + y = 7 and 2x - y = 2?

    Answer: x = 3, y = 4

    Adding gives 3x = 9, so x = 3; substituting gives y = 4.

  5. A system with exactly one solution is called:

    Answer: Consistent and independent

    A system with exactly one solution is consistent (a solution exists) and independent (distinct lines).

  6. In the system y = 4x - 3 and y = 4x + 1, how many solutions exist?

    Answer: None

    Both lines have slope 4 but different intercepts, making them parallel with no intersection.