Exercise 13 Page 267

We are asked to describe the advantages and disadvantages of solving a System of Linear Equations by graphing. This method consists of visually finding the point of intersection of two lines.

Advantages

Let's first consider the advantages.

• If we do not like algebra, the most obvious advantage is that we do not have to deal with it! We just need to draw both lines on the same plane and state the coordinates of the intersection, if any.
• Without too much work, the solution we get by graphing is the same as the one we would get using any other method.
• This method helps us to understand that, when solving a system, we are actually finding the point of intersection of two lines. Therefore, we have a clear picture of what we are doing.

We can see an example. y=x-1 & (I) y=- x+1 & (II) Equation (I) represents a line with slope 1 and y-intercept - 1.

Equation (II) represents a line with slope - 1 and y-intercept 1.

We can see above that the point of intersection of the lines, which is the solution of the system, is (1,0). However, as any other method, it has its disadvantages.

Disadvantages

Now, let's consider the potential disadvantages.

• If the lines are not given in slope-intersect form, we will have to deal with algebra in order to isolate y.
• If the coordinates of the point of intersection are not integers, and we are looking for an accurate decimal answer, we might not be able to achieve it.

Let's consider another example, this time to show the disadvantages. y=2x & (I) 3y+6x=9 & (II) First of all, we can see that the y-variable is not isolated in Equation (II). Therefore, we will have to use some algebra to isolate it.

We found that Equation (II) can be rewritten as y=- 2x+3. Let's draw the graph of this line, where the slope is - 2 and the y-intercept is 3.

Finally, let's draw the graph of the line represented by Equation (I), where the slope is 2 and the y-intercept is 0.

As we can see above, we cannot determine accurate coordinates for the intersection. Note that these are the advantages and disadvantages we found for this method. However, it depends on us to find what we consider to be advantages and disadvantages!