Algebra Know-It-ALL

In the first equation, we can subtract x from each side to get

y=−x+ 44

We can substitute the quantity (−x+ 44) for y in the second original equation, getting

x− (−x+ 44) = 10

This can be rewritten as

x+ [−1(−x+ 44)] = 10

and simplified to

x+x− 44 = 10

When we add 44 to each side and note that x+x= 2 x, we obtain

2 x= 54

This tells us that x= 27. Now we can plug this into the SI equation and solve for y, as follows:

y=−x+ 44

=− 27 + 44

= 17

When we check back and compare this with solution to Prob. 1, we see that the answers are the same: x= 27 and y= 17.

Let’s call the numbers x and y, as we did in Prob. 4. Here again are the equations that
we must solve as a two-by-two linear system:

x+y=− 83

and

x−y= 13

The first equation can be put into SI form if we subtract x from each side. That gives us

y=−x− 83

When we substitute (−x− 83) for y in the second equation, we get

x− (−x− 83) = 13

This can be rewritten as

x+ [−1(−x− 83)] = 13

Chapter 16 643