# Worksheet: Solving Systems of Equations Graphically

Q1:

Find the solution set of the two equations represented by the and .

• A
• B
• C
• D
• E

Q2:

Use the shown graph to solve the given simultaneous equations.

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

Q3:

Use the shown graph to solve the given simultaneous equations.

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

Q4:

Use the shown graph to solve the simultaneous equations

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

Q5:

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

• A
• B
• C
• D
• E

Q6:

By plotting the graphs of and , determine the pair of - and -coordinates that satisfies both equations simultaneously.

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

Q7:

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

• A
• B
• C
• D
• E

Q8:

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

• A
• B
• C
• D
• E

Q9:

Plot the graphs of the 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.

Q10:

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

• A
• B
• C
• D
• E

Q11:

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

• Ano
• Byes,
• Cyes, (1, 7)
• Dyes,
• Eyes, (7, 1)

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:

By graphing the functions and , state the point at which they intersect.

• A
• B
• C
• D

Q14:

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

• A
• B
• C
• D
• E

Q15:

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

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

Q16:

The given graph shows the lines and . Determine the point whose coordinates are solutions to both equations simultaneously.

• A
• B(17, 6)
• C
• D(6, 17)
• E

Q17:

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

• A(1, 3)
• B(3, 7)
• C
• D
• E(3, 1)

Q18:

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

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

Q19:

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

• A
• B
• C
• D
• E

Q20:

Use the shown graph to solve the given simultaneous equations.

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

Q21:

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

• A ,
• BThere are infinitely many solutions as both equations represent the same line.
• C ,
• DThere are no solutions as both equations represent parallel lines.
• E ,

Q22:

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

• A
• B
• C
• D
• E

Q23:

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

Q24:

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

• A ,
• B ,
• C ,
• D ,
• E ,

Q25:

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

• Ayes,
• Byes,
• Cno
• Dyes,
• Eyes,