Algebra Know-It-ALL

272 Two-by-Two Linear Graphs

upward. How about 3 units to the right? Will the w value go off the scale? Let’s plug in v= 3

and see what we get:

w= 7 × 3 − 10

= 21 − 10

= 11

It’s still in the field of view, so we can plot (3, 11) on the plane as a small open circle, and draw

the line for the first equation through it and (0, −10).

There’s no doubt that we need to find a more distant point on the line for the second

equation. In SI form, that equation is

w= (−1/2)v− 5

so the slope is −1/2. Knowing this and the w-intercept, we can get a good idea of the position

and orientation of the line. It passes through the point (0, −5), ramps gradually downward as

v

w

(0,–10)

(0,–5)

Solution =

(2/3,–16/3)

(–12,1)

(3,11)

–7v+w+ 10 = 0

w= 7v– 10

4 v+ 8w= –40

w= (–1/2)v– 5

Each axis

increment

is 2 units

Figure 17-5 Graphs of − 7 v+w+ 10 = 0 and

4 v+ 8 w=−40 as a two-by-two linear

system where the independent variable is v

and the dependent variable is w. On both

axes, each increment represents 2 units.

The SI forms of the equations are shown

below the originals.