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 .