# Lesson Worksheet: Solving Systems of Linear Equations Graphically Mathematics • 8th Grade

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 and . • A
• B
• C
• D
• E

Q2:

Use the shown graph to solve the 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:

Use the shown graph to solve the given simultaneous equations. • A and
• B and
• C and
• D and
• E and

Q6:

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

• A • B • C • D • E Q7:

Which of the following sets of simultaneous equations could be solved using the given graph? • A
• B
• C
• D
• E

Q8:

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

• A(1, 3)
• B
• C(3, 1)
• D
• E(3, 7)

Q9:

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

• AThere are infinitely many solutions as both equations represent the same line.
• B,
• C,
• D,
• 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 and then solve the system.

• A,
• B,
• C,
• D,
• E,

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

Q13:

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

Q14:

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

• A
• B
• C
• D
• E

Q15:

Using the graph, determine which of the following is a sensible estimate for the solution to the simultaneous equations • A
• B
• C
• D
• E

Q16:

Using the graph, determine which of the following is a sensible estimate for the solution to the simultaneous equations • A
• B
• C
• D
• E

Q17:

The given graph shows the lines and . Determine the point whose coordinates satisfy both equations simultaneously. • A
• B
• C
• D
• E

Q18:

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, 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 • A
• B
• C
• D
• E

Q20:

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

• A,
• BThere are infinitely many solutions as both equations represent the same line.
• C,
• D,
• 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,
• BNo
• CYes, (7, 1)
• DYes,
• EYes, (1, 7)

Q22:

The given graph shows the lines and . Determine the point whose coordinates satisfy both equations simultaneously. • A
• B
• C
• D
• E

Q23:

The given graph shows the lines and . Determine the point whose coordinates are solutions to both equations simultaneously. • A
• B(6, 17)
• C(17, 6)
• D
• E

Q24:

Do the simultaneous equations and plotted in the given graph have a solution? If yes, find it. • AYes,
• BYes,
• CYes,
• DNo
• EYes,

Q25:

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

• A
• B
• C
• D(1, 1)
• E