Worksheet: Solving Systems of Linear Equations Graphically

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.

  • A π‘₯ = 1 . 5 and 𝑦=3
  • B π‘₯ = 1 and 𝑦=1
  • C π‘₯ = βˆ’ 2 and 𝑦=3
  • D π‘₯ = 1 and 𝑦=βˆ’2
  • E π‘₯ = 0 and 𝑦=3

Q3:

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

  • A π‘₯ = 1 and 𝑦=2
  • B π‘₯ = 0 and 𝑦=2
  • C π‘₯ = 2 and 𝑦=2
  • D π‘₯ = 2 and 𝑦=0
  • E π‘₯ = 2 and 𝑦=1

Q4:

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

  • A π‘₯ = 7 and 𝑦=3
  • B π‘₯ = βˆ’ 2 and 𝑦=3
  • C π‘₯ = 0 and 𝑦=3
  • D π‘₯ = 3 and 𝑦=0
  • E π‘₯ = 3 and 𝑦=7

Q5:

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

  • A π‘₯ = 2 and 𝑦=1
  • B π‘₯ = 3 and 𝑦=3
  • C π‘₯ = 3 and 𝑦=0
  • D π‘₯ = 0 and 𝑦=3
  • E π‘₯ = 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?

  • A 𝑦 = 2 π‘₯ βˆ’ 4 , 𝑦 = βˆ’ π‘₯ + 5
  • B 𝑦 = βˆ’ 4 π‘₯ + 2 , 𝑦 = 5 π‘₯ βˆ’ 1
  • C 𝑦 = βˆ’ 4 π‘₯ + 2 , 𝑦 = 5 π‘₯ + 1
  • D 𝑦 = 2 π‘₯ βˆ’ 4 , 𝑦 = π‘₯ + 5
  • E 𝑦 = 2 π‘₯ + 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.
  • B π‘₯ = 1 , 𝑦 = βˆ’ 2
  • C π‘₯ = 0 , 𝑦 = 7
  • D π‘₯ = 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.

  • A π‘₯ = 0 , 𝑦 = 7 2
  • B π‘₯ = 2 , 𝑦 = 1 1
  • C π‘₯ = βˆ’ 2 , 𝑦 = 1 1
  • D π‘₯ = 2 , 𝑦 = 5
  • E π‘₯ = βˆ’ 7 2 , 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.

  • A 0 . 5 < π‘₯ < 0 . 7 5 and βˆ’3<𝑦<βˆ’1
  • B βˆ’ 1 < π‘₯ < βˆ’ 0 . 7 5 and 0.5<𝑦<0.75
  • C βˆ’ 0 . 7 5 < π‘₯ < βˆ’ 0 . 5 and 0.75<𝑦<1
  • D 0 . 5 < π‘₯ < 0 . 7 5 and βˆ’1<𝑦<βˆ’0.75
  • E 0 . 7 5 < 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.

  • A π‘₯ = 5 . 6 , 𝑦 = 2 . 4
  • B π‘₯ = 5 . 4 , 𝑦 = 3 . 1
  • C π‘₯ = 5 . 4 , 𝑦 = 2 . 9
  • D π‘₯ = 5 . 7 , 𝑦 = 2 . 9
  • E π‘₯ = 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.

  • A π‘₯ = 2 . 7 , 𝑦 = 2 . 3
  • B π‘₯ = 2 . 6 , 𝑦 = 2 . 4
  • C π‘₯ = 2 . 2 , 𝑦 = 2 . 8
  • D π‘₯ = 2 . 9 , 𝑦 = 2 . 1
  • E π‘₯ = 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.

  • A π‘₯ = βˆ’ 0 . 5 , 𝑦 = βˆ’ 4 . 5
  • B π‘₯ = 0 . 5 , 𝑦 = βˆ’ 4 . 5
  • C π‘₯ = 0 . 5 , 𝑦 = βˆ’ 5 . 5
  • D π‘₯ = 0 . 5 , 𝑦 = 5 . 5
  • E π‘₯ = 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.

  • A π‘₯ = βˆ’ 2 , 𝑦 = 3
  • BThere are infinitely many solutions as both equations represent the same line.
  • C π‘₯ = 2 , 𝑦 = βˆ’ 9
  • D π‘₯ = 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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