1. (a) y = −12 (Clear fractions first.)
(b) No solution
2. Unknowns:
Tacoma Area = T
Seattle Area = T + 80
Equation: T + T + 80 = 205
Solution: Tacoma has an area of 62.5 square miles and Seattle has an area
of 142.5 square miles.
3. • x = −2 This is vertical line whose points all have an
x- coordinate of −2. The x- intercept for this
line is (−2, 0). This line has no y-intercept. The slope of this line is
undefined. (Pick any two points
on this line and you will see that when you compute the slope between them, the
expression is undefined .)
• y = 5 This is horizontal line whose points all have an
y-coordinate of 5. The y-intercept for this line
is (0, 5). This line has no x-intercept. The slope of this line is 0. (Pick any
two points on this line and
you will see that when you compute the slope between them, the expression is
always 0.)
• 3x − 4y = 12 ==> y = 3/4x − 3 From the equation in
slope-intercept form, we can see that this is
a line with slope 3/4 and y-intercept (0,−3). The x-intercept is (4, 0). (Plug
in y = 0 and solve for x .)
4. (a) Equation in point-slope: y − 6 = −4(x − 1) ==>
Equation in slope-intercept: y = −4x + 10
(b) The slope of the line we are writing the equation for is 1/4 since it is
perpendicular to a line of slope −4.
Equation in point-slope: y + 2 = 1/4 (x − 8) ==> Equation in slope-intercept: y
= 1/4x − 4
5. (a) Using the graphing , substitution, or elimination
method , you should get that there are an infinite number
of solutions. (Same line.)
(b) Using the graphing, substitution, or elimination method, you should get that
the solution is (0, 3).
6.
7.
8.
(a) y = ±2 (Factoring, square root property , completing the square, or quadratic
formula )
(b) t = 5 or t = −3 (Factoring, completing the square, or quadratic formula)
(c) 
(Completing the square or the quadratic
formula)
(d) No real solutions (Completing the square or the quadratic formula - Square
root of a negative number )
(e) 
(Completing the square or the quadratic
formula - Put in standard form first.)
9. You can solve this using just one variable or with two
variables .
• One variable :
Unknowns: Amount in 4% account = x, Amount in 9% account = 3000 − x
Equation: 0.04x + 0.09(3000 − x) = 200 ==> x = 1400
Solution: Ernie invested $1400 at 4% and $1600 at 9%.
• Two variables:
Unknowns: Amount in 4% account = x, Amount in 9% account = y
Equations: x + y = 3000,
0.04x + 0.09y = 200 ==> x = 1400, y = 1600
(Using substitution or elimination )
Solution: Ernie invested $1400 at 4% and $1600 at 9%.
10. You can solve this using just one variable or with two
variables.
• One variable:
Unknowns: Speed of s lower bus = x, Speed of faster bus = x + 20
Equation: 3x + 3(x + 20) = 400 ==> x = 340/6 , which simplifies to x =
170/3 ≈ 56.67 mph
Solution: The slower bus travels at a speed of 170/3 ≈ 56.67 mph. The
faster bus travels at a speed
of 230/3 ≈ 76.67 mph.
Additionally, the slower bus travels a distance of (170/3) ·3 = 170 miles and
the faster bus travels a distance
of (230/3) ·3 = 230 miles. (Using d = r · t)
• Two variables:
Unknowns: Speed of slower bus = x, Speed of faster bus = y
Equation: y = x + 20,
3x + 3y = 400 ==> x = 170/3 , y = 230/3
Solution: The slower bus travels at a speed of 170/3 ≈ 56.67 mph. The
faster bus travels at a speed
of 230/3 ≈ 76.67 mph.
Additionally, the slower bus travels a distance of (170/3) ·3 = 170 miles and
the faster bus travels a distance
of (230/3) ·3 = 230 miles. (Using d = r · t)
11. Using the Pythagorean theorem:
Since x = −1 does not make sense for our triangle, we have that x = 5 and the
sides of the triangle have the
lengths 5, 12, and 13.
12.
(a) 96 feet (Evaluate h = −16t^2 + 80 at t = 2.)
(b) The rocket lands at 5 seconds. (Solve 0 = −16t^2 + 80t
since h = 0. You can factor, complete the
square, or use the quadratic formula to solve.)
(c) The rocket will be 36 feet at 1/2 second and 9/2
seconds. (Solve 36 = −16t^2 + 80t since h = 36. You
can factor, complete the square, or use the quadratic formula to solve.)
