Linear equations and systems

Practice sheet

Fresh questions from the whole chapter, to do on paper.

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  1. Solve 3x+3=−183x + 3 = -18. x=  ?x = \;?
  2. Solve 4x+8=3x+94x + 8 = 3x + 9. x=  ?x = \;?
  3. Solve 6(x+4)=306(x + 4) = 30. x=  ?x = \;?
  4. How many solutions has 3(x+2)=3x+63(x + 2) = 3x + 6?
    1. Infinitely many
    2. Exactly one
    3. No solution
  5. How many solutions has 2x+7=2x+132x + 7 = 2x + 13?
    1. No solution
    2. Exactly one
    3. Infinitely many
  6. What number cc makes 2x+7=cx+192x + 7 = cx + 19 have no solution?
  7. How many solutions has the system y=5x+6y = 5x + 6 and y=5x+7y = 5x + 7?
    1. No solution
    2. Exactly one
    3. Infinitely many
  8. How many solutions has the system y=6x+4y = 6x + 4 and 12x−2y=−812x - 2y = -8?
    1. Infinitely many
    2. No solution
    3. Exactly one
  9. How many solutions has the system y=3x+2y = 3x + 2 and y=−3x+9y = -3x + 9?
    1. Exactly one
    2. No solution
    3. Infinitely many
  10. Solve the system y=2x+4y = 2x + 4 and 3x+y=243x + y = 24. x=  ?x = \;?
  11. Solve the system y=2x+4y = 2x + 4 and 2x+y=242x + y = 24. y=  ?y = \;?
  12. Solve the system x=3yx = 3y and x+y=24x + y = 24. y=  ?y = \;?