Algebra Know-It-ALL

638 Worked-Out Solutions to Exercises: Chapters 11 to 19

Let’s get the equations into SI form. In the first equation, we can subtract x from each

side to get

y=−x+ 44

In the second equation, we can subtract x from each side and then multiply through by

−1 to obtain

y=x− 10

Mixing the right sides of these two SI equations produces this:

−x+ 44 =x− 10

Adding 10 to each side gives us

−x+ 54 =x

Adding x to each side, we get

54 = 2 x

Dividing through by 2, we determine that x= 27. We can plug this into either of the SI

equations to solve for y. Let’s use the second one. We have

y=x− 10

= 27 − 10

= 17

The two numbers are 27 and 17.

2. Again, let’s call the numbers x and y. We are told that these two facts are true:

x+y= 100

and

y= 6 x

Actually, we could just as well say that x= 6 y; it doesn’t matter. Let’s stick with the equations

above. The first equation can be put into SI form by subtracting x from each side. That gives us

y=−x+ 100

The second equation is already in SI form (the y-intercept is 0). Mixing the right-hand

sides, we obtain

−x+ 100 = 6 x