These are both functions of v. If we put these equations into SI form with v rather than w as the dependent
variable, we obtain the inverse relations. Here are the manipulations, starting with the original equations:
− 7 v+w+ 10 = 0
− 7 v+ 10 =−w
− 7 v=−w− 10
7 v=w+ 10
v= (1/7)w+ 10/7
and
4 v+ 8 w=− 40
4 v=− 8 w− 40
v= (−8/4)w− 40/4
v=− 2 w− 10
These inverse relations are both functions of w. Can you see why?
We Couldn’t Solve, but We Can Graph
In exercises 5, 6, and 7 at the end of Chap. 16, we scrutinized a two-by-two linear system. We
could not solve it. Here’s the pair of equations:
2 x+y= 3
and
6 x+ 3 y= 12
Let’s graph these equations. This will help us see why no ordered pair (x,y) satisfies them as a
system.
Find two points for each line
If we consider x as the independent variable and y as the dependent variable, then the SI version
of the first equation is
y=− 2 x+ 3
and the SI version of the second equation is
y=− 2 x+ 4
They-intercepts are 3 and 4, respectively. That means the point (0, 3) lies on the line for the
first equation, and the point (0, 4) lies on the line for the second equation.
We Couldn’t Solve, but We Can Graph 275
