Challenge 41. Reasoning C onsider th e system at th e right. y = gx + 3
y = hx + 7
a. If g > h, will the system always, sometimes, or never h a v e e x a c tly o n e s o l u t io n?
Explain your reasoning.
b. If g £ h, will th e system always, sometimes, or never have infinitely m any
solutions? Explain your reasoning.- Hiking Two hikers are walking along a m arked trail. The first hiker starts at a
p o in t 6 m i from th e b eginning of th e trail an d walks at a sp ee d of 4 m i /h. At the
sam e time, the seco n d hiker starts 1 m i from th e beginning a n d walks at a speed
of 3 m i/h.
a. W hat is a system of equations th a t m odels th e situation?
b. G raph th e two eq u atio n s a n d find th e intersection point.
c. Is th e intersection p o in t m eaningful in this situation? Explain.
^SAT/ACT
Extended. R e s p o n s e
St an d ar d i zed Test Pr ep
- W hich o rdered pair is th e solution of th e system? 2x + 3y = - 1 7
3x + 2y= -8
C D (2, - 7 ) C D ( - 4 , 2) C D ( - 2 , - 1 ) - W hich expression is equivalent to 5(m - 12) + 8?
CD 5m - 68 CD 5m - 20 CD 5m — 4 - The costs for parking in two different parking garages are given
in th e table at th e right.
a. W hat is a system of equations th a t m odels th e situation?
b. How m any hours of parking w ould cost th e sam e parking in
either garage?
c. If you n e e d e d to park a car for 3 h, w hich garage w ould you
choose? Why?
- d; —2 ^
CD 5m - 52Garage Parking Fees
F Garage Flat Fee Hourly F e e T
A $5 $2.50
B $20 $0Mixed Review
Graph each function by translating the graph of y = | x |.- y=|x|—2 47. y=|x| —1 48. y = | x + 3|
Find the slope of a line that is parallel to the graph of the equation.- y = x + 3 51.y= -|x-4 52. 3y + 2 x = 7
Get Read y! To p r e p a r e f o r Lesson 6 - 2 , d o E x e rc is e s 5 4 - 5 7.
Solve each equation fory.- 4x + 2y = 38 55. | x + | y = 5 cc 3 56. ^y = gx^4
See Lesson 5-8.- y = |x + 2|
See Lesson 5-6.- 3x = 5 y + 10
See Lesson 2-5.- 1.5x — 4.5y = 21
c
PowerAlgebra.com Lesso n 6-1 So lvin g Syst em s b y Gr ap h i n g^369