Algebra Know-It-ALL

251

CHAPTER

16 Two-by-Two Linear Systems

In Chap. 12, we saw how we can solve first-degree equations in one variable. Now it’s time to

work with pairs of linear equations in two variables, also known as two-by-two linear systems.

Solving a linear system involves reducing it to first-degree equations, one for each of the

variables.

Morph and Mix

When we want to solve a two-by-two linear system, we can put both equations into slope-

intercept (SI) form. Then we can take the right sides of the resulting equations and mix them

to get a first-degree equation in one variable. We can solve that equation, and finally plug the

result into either of the SI equations to solve for the other variable.

Morph both equations into SI form

Suppose we are told to find the values of x and y such that both of the following equations

are true:

8 x+ 4 y= 16

and

7 x−y= 41

Let’s put these equations into SI form. In the first case, we start with

8 x+ 4 y= 16

Subtracting 8x from each side gives us

4 y=− 8 x+ 16

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