Lesson Worksheet: Solving Systems of Linear Equations Graphically Mathematics • 8th Grade

In this worksheet, we will practice solving a system of two linear equations by considering their graphs and identifying the point of intersection.

Q1:

Find the solution set of the two equations represented by 𝐿 and 𝐿.

  • A{(3,3)}
  • B{(3,2)}
  • C{(2,0)}
  • D{(2,3)}
  • E{(2,2)}

Q2:

Which of the following could represent a pair of simultaneous equations with no solution?

  • A(c)
  • B(b)
  • C(a)
  • D(d)

Q3:

By plotting the graphs of 𝑦=π‘₯βˆ’1 and 𝑦=5π‘₯+7, find the point that satisfies both equations simultaneously.

  • A(βˆ’2,βˆ’3)
  • B(βˆ’1,1)
  • C(1,βˆ’1)
  • D(βˆ’3,βˆ’2)
  • E(1,7)

Q4:

Use the shown graph to solve the given simultaneous equations. 𝑦=4π‘₯βˆ’2𝑦=βˆ’π‘₯+3

  • Aπ‘₯=2 and 𝑦=1
  • Bπ‘₯=3 and 𝑦=3
  • Cπ‘₯=3 and 𝑦=0
  • Dπ‘₯=0 and 𝑦=3
  • Eπ‘₯=1 and 𝑦=2

Q5:

By plotting the graphs of 12π‘₯βˆ’9𝑦=24 and 4π‘₯βˆ’3𝑦=8, determine the π‘₯- and 𝑦-coordinates of the point that satisfies both equations simultaneously.

  • AThe coordinates of the point that satisfies both equations are (0,βˆ’2).
  • BThe two lines are coincident, so there are an infinite number of solutions.
  • CThe coordinates of the point that satisfies both equations are (2,0).
  • DThe coordinates of the point that satisfies both equations are (βˆ’2,0).
  • EThe two lines are parallel, so there are no solutions.

Q6:

Using the given graph, determine whether there is a point whose coordinates satisfy the equations of both lines simultaneously. If yes, find its coordinates.

  • AThe intersection point is (0,βˆ’5).
  • BThe intersection point is (1,βˆ’2).
  • CThe two lines are parallel, so there is no such point.
  • DThe intersection point is (0,βˆ’2).
  • EThe intersection point is (3,βˆ’5).

Q7:

Plot the graphs of the simultaneous equations 𝑦=2π‘₯+7,𝑦=2π‘₯βˆ’4, and then solve the system.

  • AThere are infinitely many solutions as both equations represent the same line.
  • Bπ‘₯=1, 𝑦=βˆ’2
  • Cπ‘₯=0, 𝑦=7
  • Dπ‘₯=1, 𝑦=9
  • EThere are no solutions as both equations represent parallel lines.

Q8:

Which of the following sets of simultaneous equations could be solved using the given graph?

  • A𝑦=2π‘₯βˆ’4,𝑦=βˆ’π‘₯+5
  • B𝑦=βˆ’4π‘₯+2,𝑦=5π‘₯βˆ’1
  • C𝑦=βˆ’4π‘₯+2,𝑦=5π‘₯+1
  • D𝑦=2π‘₯βˆ’4,𝑦=π‘₯+5
  • E𝑦=2π‘₯+4,𝑦=βˆ’π‘₯+5

Q9:

Which of the following graphs could be used to help solve the set of simultaneous equations 𝑦=3π‘₯βˆ’4,𝑦=βˆ’12π‘₯+3?

  • A
  • B
  • C
  • D
  • E

Q10:

Use the shown graph to find appropriate ranges for the solutions to the simultaneous equations 𝑦=3π‘₯βˆ’3,5π‘₯+7𝑦=βˆ’2.

  • A0.5<π‘₯<0.75 and βˆ’3<𝑦<βˆ’1
  • Bβˆ’1<π‘₯<βˆ’0.75 and 0.5<𝑦<0.75
  • Cβˆ’0.75<π‘₯<βˆ’0.5 and 0.75<𝑦<1
  • D0.5<π‘₯<0.75 and βˆ’1<𝑦<βˆ’0.75
  • E0.75<π‘₯<1 and βˆ’0.75<𝑦<βˆ’0.5

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