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Worksheet: Solving Equations Graphically

Q1:

The diagram shows the graph of . What is the solution set of the equation ?

  • A
  • B
  • C
  • D
  • E

Q2:

The graph shows the curve with equation . What is the solution set of the equation ?

  • A
  • B
  • C
  • D

Q3:

The diagram shows the graph of . What is the solution set of the equation ?

  • A
  • B
  • C
  • D
  • E

Q4:

The diagram shows the graph of . What is the solution set of the equation ?

  • A
  • B
  • C
  • D
  • E

Q5:

Consider the equation .

Find the solutions when .

  • A,
  • B,
  • C,
  • D,
  • E,

Find the -solutions when .

  • A,
  • B,
  • C,
  • D,
  • E,

Find the -solutions when .

  • A,
  • B,
  • C,
  • D,
  • E,

The solutions found can be plotted in plane as seen in the given figure. What will be true of the plot of any other solution?

  • AThey will lie on the -axis.
  • BThey will not lie on the curve.
  • CThey will lie on the curve.
  • DThey will not lie in the same quadrant.
  • EThey will lie in the same quadrant.

Q6:

Work out the solutions of for the given values of .

.

  • A,
  • B,
  • C,
  • D,
  • E,

.

  • A,
  • B,
  • C,
  • D,
  • E,

.

  • A,
  • B,
  • C,
  • D,
  • E,

.

  • A
  • B
  • C
  • D
  • E

The solutions found can be plotted in plane as seen in the given figure. What will be true of the plot of any other solution?

  • AThey will lie on the -axis.
  • BThey will not lie on the curve.
  • CThey will lie on the curve.
  • DThey will not lie in the same quadrant.
  • EThey will lie in the same quadrant.

Q7:

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

Q8:

The given figure shows the graphs of the functions and . What are the points where ?

  • A,
  • B,
  • C,
  • D,
  • E,

Q9:

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

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

Q10:

Use the shown graph to solve the given simultaneous equations.

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

Q11:

The given figure shows the graphs of the functions and . What are the points where