Lesson Worksheet: Consistency and Dependency of Linear Systems Mathematics • 8th Grade

In this worksheet, we will practice determining the number of solutions for a system of linear equations and whether each system is consistent, inconsistent, or dependent.


How many solutions are there to the simultaneous equations π‘₯+7𝑦=20 and 2π‘₯+14𝑦=40?

  • Atwo solutions
  • Ban infinite number of solutions
  • Czero
  • Da unique solution


If the simultaneous equations 6π‘₯+7𝑦=2 and 18π‘₯+π‘˜π‘¦=6 have an infinite number of solutions, what is the value of π‘˜?


Is there a solution to the system of equations 3π‘₯+4𝑦=10,3π‘₯+4𝑦=βˆ’12? If yes, what is it?

  • AYes, π‘₯=1,𝑦=2
  • BNo
  • CYes, π‘₯=3,𝑦=4
  • DYes, π‘₯=2,𝑦=1
  • EYes, π‘₯=4,𝑦=3


What is the value of π‘˜ for which the simultaneous equations π‘₯+2𝑦=1 and 5π‘₯+π‘˜π‘¦=5 do not have a unique solution?


What is true, in two dimensions, for two linear equations that simultaneously have infinitely many solutions?

  • ABoth equations represent parallel lines.
  • BBoth equations represent perpendicular lines.
  • CBoth equations represent horizontal lines.
  • DBoth equations represent the same line.
  • EBoth equations represent intersecting lines.


The simultaneous equations represented by the straight lines 𝐿 and 𝐿 have an infinite number of solutions. Which of the following describes the relationship between the lines 𝐿 and 𝐿?

  • AThey are coincident.
  • BThey are perpendicular.
  • CThey intersect in one point.
  • DThey are parallel.


What property, in two dimensions, is true for two lines represented by two linear equations that do NOT simultaneously have a solution?

  • AThey are perpendicular.
  • BThey are skew.
  • CThey are neither parallel nor perpendicular.
  • DThey are parallel.
  • EThey are coincident.


Find the number of solutions to the system of equations


  • AOne
  • BNone
  • CInfinitely many


Find the number of solutions to the system of equations 3𝑦=9βˆ’3π‘₯,3𝑦+3π‘₯=15.

  • AInfinitely many
  • BNone
  • COne


Is there a solution to the simultaneous equations 4π‘₯+4𝑦=20,8π‘₯+8𝑦=βˆ’2? If yes, what is it?

  • AYes, π‘₯=2,𝑦=3
  • BYes, π‘₯=4,𝑦=βˆ’1
  • CYes, π‘₯=1,𝑦=1
  • DNo
  • EYes, π‘₯=1,𝑦=4

This lesson includes 4 additional questions and 36 additional question variations for subscribers.

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