Algebra Know-It-ALL

When we morphed the above two equations before mixing them on our way to a solution,
we put them into SI form. Those SI equations, once again, are

y=− 2 x+ 4

and

y= 7 x− 41

They-intercepts are at 4 and −41. The ordered pairs for those points are (0,4) and (0,−41).
The lines intersect at the solution point where x= 5 and y=−6, corresponding to the ordered
pair (5,−6).

Connect the points

We have determined that one line passes through the points (0, 4) and (5, −6), while the other
line passes through the points (0, −41) and (5, −6). Figure 17-1 shows the graph of this system
on the Cartesian plane.

Are you confused?

In Fig. 17-1, two of the points we found are close to the origin, while the third point is far away. It’s difficult
to plot points accurately when they’re so diverse, because the increments must be large (in this case 10 units
per division). It’s also difficult to draw a line based on two points that are close together. If we want to

We Morphed, We Mi x e d, We Can Graph 265

x

y

(0,–41)

(0,4)

8 x+ 4y= 16

7 x–y= 41

Solution

= (5,–6)

(30,–56)

Each axis

increment

is 10 units

Figure 17-1 Graphs of 8x+ 4 y= 16 and 7x−y= 41

as a two-by-two linear system where

the independent variable is x and the

dependent variable is y. On both axes,

each increment represents 10 units.