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In this lesson, we will learn how to solve 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 πΏ 1 and πΏ 2 .

Q2:

Use the shown graph to solve the given simultaneous equations.

Q3:

Q4:

Use the shown graph to solve the simultaneous equations

Q5:

Q6:

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

Q7:

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

Q8:

By plotting the graphs of π¦ = β 2 π₯ + 1 and π¦ = π₯ + 4 , find the point that satisfies both equations simultaneously.

Q9:

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

Q10:

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

Q11:

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

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.

Q13:

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

Q14:

By plotting the graphs of π¦ = π₯ β 1 and π¦ = 5 π₯ + 7 , find the point that satisfies both equations simultaneously.

Q15:

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

Q16:

Q17:

The given graph shows the lines π¦ = 2 π₯ β 1 and π¦ = β 4 π₯ β 7 . Determine the point whose coordinates satisfy both equations simultaneously.

Q18:

By plotting the graphs of 3 π₯ + 2 π¦ = 1 0 and 6 π₯ + 4 π¦ = 3 0 , determine the pair of π₯ - and π¦ -coordinates that satisfies both equations simultaneously.

Q19:

Q20:

Q21:

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

Q22:

By graphing the functions π ( π₯ ) = 3 π₯ β 2 and π ( π₯ ) = 4 β π₯ , state the point at which they intersect.

Q23:

The given graph shows the lines π¦ = π₯ + 1 and π¦ = β π₯ + 3 . Determine the point whose coordinates satisfy both equations simultaneously.

Q24:

The given graph shows the lines π¦ = 3 π₯ β 1 and π¦ = 4 π₯ β 7 . Determine the point whose coordinates are solutions to both equations simultaneously.

Q25:

Do the simultaneous equations π¦ = 1 3 π₯ + 4 3 and π¦ = β 1 2 π₯ + 1 1 2 plotted in the given graph have a solution? If yes, find it.

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