CHAPTER DRILL ANSWERS AND EXPLANATIONS
Algebra Drill 1: No Calculator Section
5. C Start by multiplying the second equation by 2 to clear the fractions. The equation becomes y +
2 x = 2. To get it into the same form as the other equations, subtract 2x from both sides to get y =
–2x + 2. Set the two x expressions equal to get 3x − 1 = –2x + 2. Add 2x and 1 to both sides, so
the equation becomes 5x = 3, then divide by 5 to find that x = . Plug this value into the y = 3x
− 1 to get y = . Finally, find the value of , which
is (C).
8. B Since the question gives the value of m, the first step is to plug that value into the original
equation to get = x + 3. Now square both sides of the equation to remove the square
root: = (x + 3)^2 or –3x − 5 = x^2 + 6x + 9. Now combine like terms. If you
combine the terms on the right side of the equation, you can avoid having a negative x^2 term.
The equation becomes 0 = x^2 + 9x + 14. Factor the equation to find the roots: 0 = (x + 2)(x + 7).
The possible solutions to the quadratic are –2 and –7. Don’t forget to plug these numbers back
into the original equation to check for extraneous solutions. Begin by checking x = –2. When
you do this, you get = (–2) + 3, or = 1, or = 1, which is true. Now,
check x = –7. Set it up as = (–7) + 3, and start simplifying to get = –4.
You can technically stop simplifying here, as there is a negative number on the right-hand side
of the equal sign. Remember, when taking a square root with a radical provided, it will yield
the positive root only. So –7 cannot be part of the solution set. Be very careful of trap answer
(C), and choose (B).
11. A Use FOIL to multiply the two binomials together. The expression becomes 4 – 8i + 7i
