Question

3. Given the following system of linear equations: 2x + y = 16

x + 2y = 14

(a) Find the solution using the graphical method. Please show each step and not a screenshot of just the graph on excel

Answer 1

We need to first draw the graphs

In order to do that we need to replace values of x and y with 0 and then plot the points. Let’s take the equations one by one.

2x + y = 16

If we consider x = 0 then y = 16. This means on the y axis (vertical axis, where x = 0) the point will be 16. Similarly if y = 0 then 2x = 16 or x = 8. This means on the horizontal axis we will mark the point 8. Then we draw a line through them. It should look like the image below.

x + 2y = 14

Now, we need to repeat the same process for this equation and then plot them on the above chart. If x = 0 then 2y = 14 or y = 7. This means we need to point 7 in the vertical axis. This is also seen as (0,7). Next, if y = 0 then x =14. Thus we will mark (14,0) on the graph. Once we draw this line the image should look like shown below.

Now we need to determine the value of the point where these lines cross one another. We can count it on the horizontal plane (left to right from y axis). We can see that if we count from left to right (from the black thick line) then the value is 6. This means it is 6 units right of the point where x = 0. Thus the horizontal coordinate is x = 6

Similarly now we need to count in upward direction. We will find that it is at y = 4 or 4 units above the y = 0 line. Thus the vertical coordinate is y = 4

This means the point of intersection is (6, 4)

This gives us the solution x = 6 and y = 4 or we could write it as (6, 4)