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Worksheet: Solving System of Linear Equations by Graphing

Q1:

Use the shown graph to find appropriate ranges for the solutions to the given simultaneous equations.

  • A and
  • B and
  • C and
  • D and
  • E and

Q2:

By plotting the graphs of and , find the point that satisfies both equations simultaneously.

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

Q3:

By plotting the graphs of and , find the point that satisfies both equations simultaneously.

  • A
  • B
  • C
  • D
  • E

Q4:

Use the shown graph to solve the given simultaneous equations.

  • A and
  • B and
  • C and
  • D and
  • E and

Q5:

Use the shown graph to solve the given simultaneous equations.

  • A and
  • B and
  • C and
  • D and
  • E and

Q6:

Use the shown graph to solve the given simultaneous equations.

  • A and
  • B and
  • C and
  • D and
  • E and

Q7:

Use the shown graph to solve the given simultaneous equations.

  • A and
  • B and
  • C and
  • D and
  • E and

Q8:

Which of the following graphs could be used to help solve the given set of simultaneous equations?

  • A
  • B
  • C
  • D
  • E

Q9:

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

  • A
  • B
  • C
  • D
  • E

Q10:

Using the graph, determine which of the following is a sensible estimate for the solution to the simultaneous equations

  • A
  • B
  • C
  • D
  • E

Q11:

Plot the graphs of the simultaneous equations and then solve the system.

  • A,
  • B,
  • CThere are no solutions as both equations represent parallel lines.
  • D,
  • EThere are infinitely many solutions as both equations represent the same line.

Q12:

Using the graph, determine which of the following is a sensible estimate for the solution to the simultaneous equations

  • A
  • B
  • C
  • D
  • E

Q13:

The given graph shows the lines and . Determine the point whose coordinates satisfy both equations simultaneously.

  • A
  • B
  • C
  • D
  • E

Q14:

Answer the questions for the lines and .

Substitute into the equation and state the corresponding value of .

  • A
  • B
  • C
  • D
  • E

Substitute into the equation and state the corresponding value of .

  • A
  • B
  • C
  • D
  • E

The given graph shows the lines and . What do you notice about the point ?

  • AIt is a point that makes the two lines lie to the left of the -axis.
  • BIt is a point that makes the two lines not intersect with the -axis.
  • CIt is the intersection point of the two lines.
  • DIt is the point that makes the two lines above the -axis.
  • EIt is the center point of the two lines.

Therefore, determine the point whose coordinates are solutions to the system of equations and .

  • A
  • B
  • C
  • D
  • E

Q15:

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

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

Q16:

Plot the graphs of the equations and then solve the system.

  • A,
  • B,
  • C,
  • D,
  • E,

Q17:

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 .
  • BThe intersection point is .
  • CThe two lines are parallel, so there is no such point.
  • DThe intersection point is .
  • EThe intersection point is .