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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. Two numbers have a sum of 20 and a difference of 6. What are the numbers?

    Answer: 13 and 7

    x + y = 20 and x - y = 6 gives 2x = 26, so x = 13 and y = 7.

  2. Solve: 2x + y = 8 and x + 2y = 7

    Answer: x = 3, y = 2

    Substitute y = 8 - 2x into the second equation: x + 2(8 - 2x) = 7, giving x = 3 and y = 2.

  3. If two equations are identical, the system has:

    Answer: Infinitely many solutions

    Identical equations describe the same line, so every point on it is a solution.

  4. Solve: 5x + 2y = 20 and y = 5

    Answer: x = 2

    Substitute y = 5: 5x + 10 = 20, so 5x = 10 and x = 2.

  5. Which method is most efficient when one equation is already solved for a variable?

    Answer: Substitution

    Substitution is most efficient when a variable is isolated and can be plugged directly into the other equation.

  6. A store sells pens for $1 and notebooks for $3. If someone buys 10 items for $18, how many pens were bought?

    Answer: 6

    p + n = 10 and p + 3n = 18 gives 2n = 8, n = 4, so p = 6.