Download Geometry Algebra prep wor - Tamalpais Union High School District

Redwood High School. Department of Mathematics
REALLY Hard worker's name:____________________________
Geometry Algebra prep worksheet #4. SHOW your work in your notebook.
Write each equation in slope-intercept form. Without graphing the equations, state whether the system of equations is
consistent, inconsistent, or dependent. Also indicate whether the system has exactly one solution, no solution, or an
infinite number of solutions.
1) 7x - 2y = 9
1)
-28x + 8y = -27
2) x - 5y = 5
2x - 10y = 10
2)
3)
3)
x + 9y = 9
3x - 8y = -8
Find the solution to the system of equations by substitution.
4) x + 7y = 7
7x - 3y = -3
4)
5) x + 9y = 70
-3x + 8y = 70
5)
6) y = -4x - 14
3
y= - x+- 1
4
6)
7) x + 3y = -1
3x + 9y = -3
7)
8) y =
5
3
x4
4
8)
5x - 4y = 7
Determine the solution to the system of equations graphically. If the system is inconsistent or dependent, so state.
5
11
9) y = - x 9)
4
4
y= -
1
7
x2
2
10) 2x - 7y = 5
21y = 6x - 20
10)
11) y = 4x + 5
-8x + 2y = 10
11)
1
Solve the system of equations using the addition method.
3
12) 5x - y = 4
2
12)
2x + 2y = - 14
13)
1
1
x+ y=0
5
5
13)
1
1
3
x- y=4
4
2
14) 8x - 7y = 5
-16x + 14y = -15
14)
15) -3x + 5y = -3
10y = -6 + 6x
15)
16) -4x + 5y = 3
10y = 6 + 8x
16)
Solve the problem.
17) An investment is worth $2677 in 1993. By 1996 it has grown to $2992. Let V be the value of
the investment in the year x, where x = 0 represents 1993. Write a linear function that
models the value of the investment in the year x.
Find the least common denominator for the set of fractions.
3 1
18) ,
2 6
17)
18)
19)
1 7
,
6 5
19)
20)
14 3
,
18 30
20)
Find the x- and y-intercepts for the equation. Then graph it.
21) 16y - 4x = -8
2
22) -6x - 18y = 36
Write the two equations in slope-intercept form and then determine how many solutions the system has. Solve
23) 3x - y = 9
23)
x + 2y = 17
24) 4x - 16y = 12
1
3
y= x4
4
24)
Solve the system of equations graphically. If the system does not have a single ordered pair as a solution, state whether
the system is inconsistent of dependent.
25) 6x + y = -24
6x + 5y = 0
26) 9x - 2y = 30
4
5x + 3 y = 24
Graph the linear function by plotting the x- and y-intercepts.
27) -4x - 20y = 20
27)
Find the x- and y-intercepts for the equation. Then graph it.
28) -3x - 9y = 9
29) 15y - 3x = -6
30) y -
1
x=3
2
Solve the problem.
31) An investment is worth $2046 in 1993. By 1998 it has grown to $4406. Let V be the value of
the investment in the year x, where x = 0 represents 1993. Write a linear function that
models the value of the investment in the year x.
3
31)
32) A vendor has learned that, by pricing pretzels at $1.00, sales will reach 87 pretzels per day.
Raising the price to $1.50 will cause the sales to fall to 67 pretzels per day. The number of
pretzels, N, is a linear function of the price, x. Write a linear function that models the
number of pretzels sold per day when the price is x dollars each.
32)
33) In 1995, the average annual salary for elementary school teachers was $24,269. In 2000, the
average annual salary for elementary school teachers was $28,148. Let S be the average
annual salary in the year x, where x = 0 represents the year 1995.
a) Write a linear function that models the average annual salary for elementary school
teachers in terms of year x.
b) Use this function to determine the average annual salary for elementary school teachers
in 1997.
33)
34) The gas mileage, m, of a compact car is a linear function of the speed, s, at which the car is
driven, for 40 s 90. For example, from the graph we see that the gas mileage for the
compact car is 45 miles per gallon if the car is driven at a speed of 40 mph.
34)
i) Using the two points on the graph, determine the function m(s) that can be used to
approximate the graph.
ii) Using the function from part i, estimate the gas mileage if the compact car is traveling
75 mph. If necessary, round to the nearest tenth.
iii) Using the function from part i, estimate the speed of the compact car if the gas mileage
is 39 miles per gallon. If necessary, round to the nearest tenth.
35) In 1995, the average annual salary for elementary school teachers was $24, 269. In 2000, the
average annual salary for elementary school teachers was $28,148. Let S be the average
annual salary in the year x, where x = 0 represents the year 1995.
a) Write a linear function that models the average annual salary for elementary school
teachers in terms of year x.
b) Use this function to determine the average annual salary for elementary school teachers
in 2009.
4
35)
Answer Key
Testname: ADV ALGEBRA PREP #5
1) inconsistent
no solution
2) dependent
infinite number of solutions
3) consistent
one solution
4) (0, 1)
5) (-2, 8)
6) (-4, 2)
7) infinite number of solutions
8) no solution
9) (1, -4)
10) inconsistent
11) dependent
12) (-1, -6)
13) (-3, 3)
14) no solution
15) infinite number of solutions
16) infinite number of solutions
17) V(x) = 105x + 2677
18) 6
19) 30
20) 90
1
21) 0, - , 2, 0
2
22) (0, -2), (-6, 0)
5
Answer Key
Testname: ADV ALGEBRA PREP #5
23) One
24) Infinite number
25) (-5, 6)
26) (4, 3)
27) intercepts: (0, -1), (-5, 0)
6
Answer Key
Testname: ADV ALGEBRA PREP #5
28) (0, -1), (-3, 0)
29) 0, -
2
, 2, 0
5
30) (0, 3), (-6, 0)
31) V(x) = 472x + 2046
32) N(x) = -40x + 127
33) a) S(x) = 775.8x + 24,269
b) $25,820.60
1
34) i) m(s) = - s + 65
2
ii) 27.5 miles per gallon
iii) 52 mph
7
Answer Key
Testname: ADV ALGEBRA PREP #5
35) a) S(x) = 775.8x + 24,269
b) $35,130.20
8