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 the 𝐿 and 𝐿.

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

Q2:

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

  • Aπ‘₯=1.5 and 𝑦=3
  • Bπ‘₯=1 and 𝑦=1
  • Cπ‘₯=βˆ’2 and 𝑦=3
  • Dπ‘₯=1 and 𝑦=βˆ’2
  • Eπ‘₯=0 and 𝑦=3

Q3:

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

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

Q4:

Use the shown graph to solve the simultaneous equations 2π‘₯βˆ’3𝑦=6,7π‘₯+3𝑦=21.

  • Aπ‘₯=7 and 𝑦=3
  • Bπ‘₯=βˆ’2 and 𝑦=3
  • Cπ‘₯=0 and 𝑦=3
  • Dπ‘₯=3 and 𝑦=0
  • Eπ‘₯=3 and 𝑦=7

Q5:

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

Q6:

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

Q7:

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

Q8:

By plotting the graphs of 𝑦=βˆ’2π‘₯+1 and 𝑦=π‘₯+4, find the point that satisfies both equations simultaneously.

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

Q9:

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.

Q10:

Determine whether the simultaneous equations plotted in the given graph have a solution.

  • AThey have two solutions.
  • BThey have an infinite number of solutions.
  • CThey have a solution.
  • DThey do not have a solution.

Q11:

Plot the graphs of the equations 𝑦=2π‘₯+7,𝑦=4π‘₯+14, and then solve the system.

  • Aπ‘₯=0, 𝑦=72
  • Bπ‘₯=2, 𝑦=11
  • Cπ‘₯=βˆ’2, 𝑦=11
  • Dπ‘₯=2, 𝑦=5
  • Eπ‘₯=βˆ’72, 𝑦=0

Q12:

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).

Q13:

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

Q14:

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)

Q15:

Using the graph, determine which of the following is a sensible estimate for the solution to the simultaneous equations 2π‘₯+3𝑦=20,4π‘₯βˆ’4𝑦=11.

  • Aπ‘₯=5.6,𝑦=2.4
  • Bπ‘₯=5.4,𝑦=3.1
  • Cπ‘₯=5.4,𝑦=2.9
  • Dπ‘₯=5.7,𝑦=2.9
  • Eπ‘₯=5.9,𝑦=2.7

Q16:

Using the graph, determine which of the following is a sensible estimate for the solution to the simultaneous equations 4π‘₯+4𝑦=20,3π‘₯βˆ’4𝑦=βˆ’2.

  • Aπ‘₯=2.7,𝑦=2.3
  • Bπ‘₯=2.6,𝑦=2.4
  • Cπ‘₯=2.2,𝑦=2.8
  • Dπ‘₯=2.9,𝑦=2.1
  • Eπ‘₯=2.8,𝑦=2.3

Q17:

The given graph shows the lines 𝑦=2π‘₯βˆ’1 and 𝑦=βˆ’4π‘₯βˆ’7. Determine the point whose coordinates satisfy both equations simultaneously.

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

Q18:

By plotting the graphs of 3π‘₯+2𝑦=10 and 6π‘₯+4𝑦=30, determine the pair of π‘₯- and 𝑦-coordinates that satisfies both equations simultaneously.

  • AThe point coordinates that satisfy both equations are (5, 5).
  • BThe point coordinates that satisfy both equations are (5, 0).
  • CThe two lines are parallel, so there is no solution.
  • DThe point coordinates that satisfy both equations are (0, 5).
  • EThe two lines are coincident, so there is an infinite number of solutions.

Q19:

Using the graph, determine which of the following is a sensible estimate for the solution to the simultaneous equations 2𝑦=4π‘₯βˆ’11,3π‘₯βˆ’2𝑦=212.

  • Aπ‘₯=βˆ’0.5,𝑦=βˆ’4.5
  • Bπ‘₯=0.5,𝑦=βˆ’4.5
  • Cπ‘₯=0.5,𝑦=βˆ’5.5
  • Dπ‘₯=0.5,𝑦=5.5
  • Eπ‘₯=βˆ’0.5,𝑦=4.5

Q20:

Plot the graphs of the equations 𝑦=2π‘₯+7,𝑦=βˆ’3π‘₯βˆ’3, and then solve the system.

  • Aπ‘₯=βˆ’2, 𝑦=3
  • BThere are infinitely many solutions as both equations represent the same line.
  • Cπ‘₯=2, 𝑦=βˆ’9
  • Dπ‘₯=1, 𝑦=9
  • EThere are no solutions as both equations represent parallel lines.

Q21:

Do the simultaneous equations plotted in the given graph have a solution? If yes, find it.

  • AYes, (βˆ’3,βˆ’2)
  • BNo
  • CYes, (7, 1)
  • DYes, (βˆ’2,βˆ’3)
  • EYes, (1, 7)

Q22:

The given graph shows the lines 𝑦=π‘₯+1 and 𝑦=βˆ’π‘₯+3. Determine the point whose coordinates satisfy both equations simultaneously.

  • A(2,1)
  • B(1,3)
  • C(1,2)
  • D(0,3)
  • E(1,0)

Q23:

The given graph shows the lines 𝑦=3π‘₯βˆ’1 and 𝑦=4π‘₯βˆ’7. Determine the point whose coordinates are solutions to both equations simultaneously.

  • A(0,βˆ’7)
  • B(6, 17)
  • C(17, 6)
  • D(βˆ’7,2)
  • E(2,βˆ’7)

Q24:

Do the simultaneous equations 𝑦=13π‘₯+43 and 𝑦=βˆ’12π‘₯+112 plotted in the given graph have a solution? If yes, find it.

  • AYes, (5,3)
  • BYes, (2,6)
  • CYes, (5,5)
  • DNo
  • EYes, (3,5)

Q25:

By plotting the graphs of 𝑦=2π‘₯βˆ’1 and 𝑦=5π‘₯βˆ’4, find the point that satisfies both equations simultaneously.

  • A(0,βˆ’4)
  • B(βˆ’1,βˆ’1)
  • C(βˆ’1,βˆ’4)
  • D(1, 1)
  • E(0,βˆ’1)

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