6. An oil tank holds 50 litres of oil. The owner of the tank notices a leak that is causing a loss of 5 litres of oil a day.
(i) Write an equation to represent this situation. (ii) Draw a graph to represent the situation. (iii) Use your graph to work out how many days it will take for the tank to become half full.
7. A hotel needs to arrange tables to seat 180 people for a function. Tables come in two sizes: small tables seat 4 people and large tables seat 6 people.
(i) By letting x be the number of tables that seat 4 people, and y be the number of tables that seat 6 people, write an equation to represent this situation.
(ii) Find the x- and y-intercepts of the graph of the equation. (iii) Draw a graph of the equation. (iv) Give three possible combinations of tables seating 4 or 6 that can be used to seat all 180 people.
31.7 Point of intersection of two lines (simultaneous equations)
By the end of this section you should be able to:
● fi nd the point of intersection of two lines both graphically and algebraically
The point of intersection of two lines is the point ( x, y ) at which the two lines cross.
To fi nd the point of intersection graphically we draw both lines on the same axes and scales and write down the coordinates of the point where the two lines cross.
The point of intersection is the only point that will satisfy the equations of both lines at the same time (simultaneously).
In Section B, Unit 18, we learned how to fi nd the point of intersection using graphing methods and by solving simultaneous equations in algebra.
Worked example 1 (i) Using the same axes and scale, draw a graph of the following lines. 2x + y − 3 = 0
3x − 4y − 10 = 0 (ii) Use the graph to fi nd the point of intersection of these lines. Solution y 2x + y – 3 = 0 ( 0, 3 − 2