# Worksheet: Solving Systems of Linear Equations Graphically

In this worksheet, we will practice solving a system of two linear equations by considering their graphs and identifying the point of intersection.

**Q6: **

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

- A
- B
- C
- D
- E

**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

**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

**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