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