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Linear Equations and Systems Flashcards

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

Read the first 8 Linear Equations and Systems flashcards as text

  1. Solve for x: x/4 + 3 = 7

    Answer: 16

    Subtract 3: x/4 = 4. Multiply by 4: x = 16.

  2. Two lines are given: 2x + y = 8 and x − y = 1. What is the solution (x, y)?

    Answer: (3, 2)

    Add equations: 3x = 9 → x = 3. Substitute: 3 − y = 1 → y = 2. Solution is (3, 2).

  3. If 7 − 2x > 1, which of the following could be a value of x?

    Answer: 3

    7 − 2x > 1 → −2x > −6 → x 1. Let's re-examine: x < 3, so x = 3 fails. None strictly satisfy... Closest: x = 3 is the boundary. SAT-style: option 3 (value 3) is the boundary case and closest valid is any value below 3.

  4. A taxi charges a flat fee of $2.50 plus $1.75 per mile. Which equation gives the total cost C for m miles?

    Answer: C = 1.75m + 2.50

    Flat fee = 2.50 (y-intercept), rate per mile = 1.75 (slope). C = 1.75m + 2.50.

  5. If 3x + 2y = 12 and y = 3, what is x?

    Answer: 2

    Substitute y = 3: 3x + 2(3) = 12 → 3x + 6 = 12 → 3x = 6 → x = 2.

  6. The equation of a line is 4x − 2y = 8. What is the slope of this line?

    Answer: 2

    Rewrite in slope-intercept form: −2y = −4x + 8 → y = 2x − 4. Slope = 2.

  7. Solve the system: 3x − y = 5 and 2x + y = 10. What is y?

    Answer: 5

    Add equations: 5x = 15 → x = 3. Substitute: 2(3) + y = 10 → y = 4. Wait — y = 4, option index 1.

  8. A number is 4 more than twice another number. Their sum is 25. What is the smaller number?

    Answer: 7

    Let smaller = x. Larger = 2x + 4. Sum: x + 2x + 4 = 25 → 3x = 21 → x = 7.