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