Algebra Know-It-ALL

326 Review Questions and Answers

That’s in the form we want! Again from Answer 15-4, the slope-intercept form of the equation

for line QR is

y= (5/2)x− 1

When we multiply each side by 2, we get

2 y= 5 x− 2

Subtracting 5x from each side, we obtain

− 5 x+ 2 y=− 2

That’s in the form we want! Once again referring to Answer 15-4, the slope-intercept form of

the equation for line PR is

y=x+ 2

Subtracting x from each side gives us

−x+y= 2

That’s in the form we want!

Chapter 16

Question 16-1

In Chap. 16, we learned how a two-by-two linear system in variables x and y can be solved by

the following process:

• Morph both equations into SI form with y all by itself on the left side of the
  equals sign.


• Mix the two equations to get a first-degree equation in x.


• Solve the first-degree equation for x.


• Substitute that solution back into one of the SI equations to solve for y.

How can we solve such a system by morphing and mixing alone, without substituting either

variable for the other?

Answer 16-1

We can go through the morph-and-mix process twice, first for one variable and then for the

other. We proceed like this:

• Morph both equations into SI form with y all by itself on the left side of the
  equals sign.


• Mix the two equations to get a first-degree equation in x.