Worksheet: Solving Systems of Linear Equations Graphically

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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=−2𝑥+3,𝑦=3𝑥−2.

  • A𝑥=1.5 and 𝑦=3
  • B𝑥=1 and 𝑦=1
  • C𝑥=−2 and 𝑦=3
  • D𝑥=1 and 𝑦=−2
  • E𝑥=0 and 𝑦=3

Q3:

Use the shown graph to solve the given simultaneous equations. 𝑦=−2𝑥+2𝑦=3𝑥+2

  • A𝑥=1 and 𝑦=2
  • B𝑥=0 and 𝑦=2
  • C𝑥=2 and 𝑦=2
  • D𝑥=2 and 𝑦=0
  • E𝑥=2 and 𝑦=1

Q4:

Use the shown graph to solve the simultaneous equations 2𝑥−3𝑦=6,7𝑥+3𝑦=21.

  • A𝑥=7 and 𝑦=3
  • B𝑥=−2 and 𝑦=3
  • C𝑥=0 and 𝑦=3
  • D𝑥=3 and 𝑦=0
  • E𝑥=3 and 𝑦=7

Q5:

Use the shown graph to solve the given simultaneous equations. 𝑦=4𝑥−2𝑦=−𝑥+3

  • A𝑥=2 and 𝑦=1
  • B𝑥=3 and 𝑦=3
  • C𝑥=3 and 𝑦=0
  • D𝑥=0 and 𝑦=3
  • E𝑥=1 and 𝑦=2

Q6:

Which of the following graphs could be used to help solve the set of simultaneous equations 𝑦=3𝑥−4,𝑦=−12𝑥+3?

  • A
  • B
  • C
  • D
  • E

Q7:

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

  • A𝑦=2𝑥−4,𝑦=−𝑥+5
  • B𝑦=−4𝑥+2,𝑦=5𝑥−1
  • C𝑦=−4𝑥+2,𝑦=5𝑥+1
  • D𝑦=2𝑥−4,𝑦=𝑥+5
  • E𝑦=2𝑥+4,𝑦=−𝑥+5

Q8:

By plotting the graphs of 𝑦=−2𝑥+1 and 𝑦=𝑥+4, find the point that satisfies both equations simultaneously.

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

Q9:

Plot the graphs of the simultaneous equations 𝑦=2𝑥+7,𝑦=2𝑥−4, and then solve the system.

  • AThere are infinitely many solutions as both equations represent the same line.
  • B𝑥=1, 𝑦=−2
  • C𝑥=0, 𝑦=7
  • D𝑥=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=2𝑥+7,𝑦=4𝑥+14, and then solve the system.

  • A𝑥=0, 𝑦=72
  • B𝑥=2, 𝑦=11
  • C𝑥=−2, 𝑦=11
  • D𝑥=2, 𝑦=5
  • E𝑥=−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,−5).
  • BThe intersection point is (1,−2).
  • CThe two lines are parallel, so there is no such point.
  • DThe intersection point is (0,−2).
  • EThe intersection point is (3,−5).

Q13:

Use the shown graph to find appropriate ranges for the solutions to the simultaneous equations 𝑦=3𝑥−3,5𝑥+7𝑦=−2.

  • A0.5<𝑥<0.75 and −3<𝑦<−1
  • B−1<𝑥<−0.75 and 0.5<𝑦<0.75
  • C−0.75<𝑥<−0.5 and 0.75<𝑦<1
  • D0.5<𝑥<0.75 and −1<𝑦<−0.75
  • E0.75<𝑥<1 and −0.75<𝑦<−0.5

Q14:

By plotting the graphs of 𝑦=𝑥−1 and 𝑦=5𝑥+7, find the point that satisfies both equations simultaneously.

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

Q15:

Using the graph, determine which of the following is a sensible estimate for the solution to the simultaneous equations 2𝑥+3𝑦=20,4𝑥−4𝑦=11.

  • A𝑥=5.6,𝑦=2.4
  • B𝑥=5.4,𝑦=3.1
  • C𝑥=5.4,𝑦=2.9
  • D𝑥=5.7,𝑦=2.9
  • E𝑥=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 4𝑥+4𝑦=20,3𝑥−4𝑦=−2.

  • A𝑥=2.7,𝑦=2.3
  • B𝑥=2.6,𝑦=2.4
  • C𝑥=2.2,𝑦=2.8
  • D𝑥=2.9,𝑦=2.1
  • E𝑥=2.8,𝑦=2.3

Q17:

The given graph shows the lines 𝑦=2𝑥−1 and 𝑦=−4𝑥−7. Determine the point whose coordinates satisfy both equations simultaneously.

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

Q18:

By plotting the graphs of 3𝑥+2𝑦=10 and 6𝑥+4𝑦=30, determine the pair of 𝑥- 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=4𝑥−11,3𝑥−2𝑦=212.

  • A𝑥=−0.5,𝑦=−4.5
  • B𝑥=0.5,𝑦=−4.5
  • C𝑥=0.5,𝑦=−5.5
  • D𝑥=0.5,𝑦=5.5
  • E𝑥=−0.5,𝑦=4.5

Q20:

Plot the graphs of the equations 𝑦=2𝑥+7,𝑦=−3𝑥−3, and then solve the system.

  • A𝑥=−2, 𝑦=3
  • BThere are infinitely many solutions as both equations represent the same line.
  • C𝑥=2, 𝑦=−9
  • D𝑥=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, (−3,−2)
  • BNo
  • CYes, (7, 1)
  • DYes, (−2,−3)
  • EYes, (1, 7)

Q22:

The given graph shows the lines 𝑦=𝑥+1 and 𝑦=−𝑥+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=3𝑥−1 and 𝑦=4𝑥−7. Determine the point whose coordinates are solutions to both equations simultaneously.

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

Q24:

Do the simultaneous equations 𝑦=13𝑥+43 and 𝑦=−12𝑥+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=2𝑥−1 and 𝑦=5𝑥−4, find the point that satisfies both equations simultaneously.

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

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