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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. If 3x + 7 = 22, what is the value of x?

    Answer: 5

    Subtract 7 from both sides: 3x = 15. Divide by 3: x = 5.

  2. A system of equations is given: y = 2x + 1 and y = -x + 7. What is the value of x at the solution?

    Answer: 2

    Set equal: 2x + 1 = -x + 7 → 3x = 6 → x = 2.

  3. The sum of two consecutive integers is 47. What is the larger integer?

    Answer: 24

    Let the integers be n and n+1. n + (n+1) = 47 → 2n + 1 = 47 → n = 23. The larger is 24.

  4. If 5(x − 2) = 3x + 6, what is x?

    Answer: 8

    Expand: 5x − 10 = 3x + 6. Subtract 3x: 2x − 10 = 6. Add 10: 2x = 16. Divide: x = 8.

  5. A store sells notebooks for $3 each and pens for $1 each. Maria spends $17 and buys 9 items total. How many notebooks did she buy?

    Answer: 4

    Let n = notebooks, p = pens. n + p = 9 and 3n + p = 17. Subtracting: 2n = 8 → n = 4.

  6. Which value of x satisfies 2(3x + 4) = 5x + 15?

    Answer: 7

    Expand: 6x + 8 = 5x + 15. Subtract 5x: x + 8 = 15. Subtract 8: x = 7.

  7. If 4x − 3y = 10 and x = 4, what is the value of y?

    Answer: 2

    Substitute x = 4: 4(4) − 3y = 10 → 16 − 3y = 10 → 3y = 6 → y = 2.

  8. A linear equation has slope 3 and passes through (0, −5). Which equation represents this line?

    Answer: y = 3x − 5

    Slope-intercept form: y = mx + b. m = 3, b = −5 (y-intercept at (0,−5)). So y = 3x − 5.