Algebra Know-It-ALL

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

Adding 15 to each side gives us

−x+ 150 =x

Adding x to each side, we get

150 = 2 x

Therefore, x= 150/2 = 75 mi/h. That’s the speed of each ball relative to the car. (You have

a pretty good throwing arm, considering you’re sitting in a car seat and throwing balls out

of an open window!) When we plug this value for x into the second SI equation, we get

y=x− 15

= 75 − 15

= 60

That means the car is moving at 60 mi/h relative to the pavement—in a forward direc-

tion, of course.

4. Let’s call the numbers x and y. We are told that both of the following facts are true:

x+y=− 83

and

x−y= 13

These equations are in the same form, so we’re ready to go. We can multiply the first

equation through by −1, getting

−x−y= 83

We add this to the second original equation:

−x−y= 83

x−y= 13

⎯⎯⎯⎯⎯

−^2 y=^96

This tells us that y= 96/(−2)=−48. Now let’s add the two original equations directly:

x+y=− 83

x−y= 13

⎯⎯⎯⎯⎯

2 x=− 70

This tells us that x=−70/2=−35.