Algebra Know-It-ALL

252 Two-by-Two Linear Systems

Dividing through by 4, we get

y=− 2 x+ 4

Now for the second equation. We begin with

7 x−y= 41

Subtracting 7x from each side, we get

−y=− 7 x+ 41

Multiplying through by −1 gives us

y= 7 x− 41

Mix the right sides and solve

Now let’s put the right side of the first SI equation on the left side of an equals sign, and the

right side of the second SI equation on the right side of the same equals sign. This produces a

first-degree equation in one variable:

− 2 x+ 4 = 7 x− 41

Now let’s solve this for x. When we subtract 7x from each side, we get

− 9 x+ 4 =− 41

We can subtract 4 from each side to obtain

− 9 x=− 45

Finally, we divide through by −9 to get

x= 5

Substitute and solve again

To solve for y, we can take either of the SI equations and plug in 5 for x. Let’s use the first one.

That gives us

y=− 2 × 5 + 4

=− 10 + 4

=− 6

We have used algebra to find that x= 5 and y=−6. We can express this as the ordered pair

(5,−6) if we imagine x as the independent variable and y as the dependent variable.