Ip (^1) Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses MATHEMATICALPRACTICES
Q Practice Solve each system using elimination. See Problems 1 and 2.
©Apply
- 3x + 3y — 27
x - 3 y = - 1 1 - 4x — 7y = 3
x - 7 y = - 1 5 - — x + 5y = 13
x — y = 15 - 5x - y = 0
3x + y = 24 - 2x + 4 y = 2 2
2x — 2y = —8 - 6x + 5y = 39
3x + 5y = 27 - Talent Show Your school's talen t show will feature 12 solo acts a n d 2 ensem ble
acts. The show will last 90 m in. The 6 solo perform ers judged b est will give
a re p eat p erform ance at a second 60-m in show, w hich will also feature the
2 ensem ble acts. Each solo act lasts x m inutes, an d each ensem ble act lasts
y minutes.
a. Write a system of equations to m odel th e situation.
b. Solve th e system from p a rt (a). How long is each solo act? How long is each
ensem ble act? - Furniture A carp en ter is designing a d rop-leaf table w ith two drop leaves of equal
size. The lengths of th e table w h en one leaf is folded up a n d w h en b oth leaves are
folded up are shown. How long is the table w h e n no leaves are folded up?
Solve each system using elimination.- 2x + 3y = 9 16. 3x + y = 5
x + 5y = 8 2x - 2y = - 2 - 3x+2y=17 19. 6x-3y=15
2 x + 5 y = 26 7x + 4 y = 1 0
Tell whether the system has one solution, infinitely many solutions, or
no solution.See Problems 3 and 4.- 6x + 4y = 42
—3x + 3y = —6 - 5x - 9y = - 4 3
3x + 8y = 68
See Problem 5.- 9x + 8y = 15
9x + 8y = 30 - 2x — 5y = 17
6x — 15y = 51 - 3x + 4y = 24
6x + 8y = 24 - 4x - 7y = 15
—8x + 14y = - 3 0 - 5x — 3y = 10
lOx + 6y = 20 - 4x - 8y = 15
- 5 x + lOy = - 3 0
- Think About a Plan A ph o to studio offers portraits in 8 X 10 a n d wallet-sized
formats. O ne custom er bo u g h t two 8 X 10 portraits an d four wallet-sized portraits
an d p aid $52. A nother custom er bought th ree 8 X 1 0 portraits an d two w allet-sized
portraits an d p aid $50. W hat is th e cost of an 8 X 10 portrait? W hat is th e cost of a
wallet-sized portrait?
- Can you elim inate a variable sim ply by adding or subtracting?
- If not, how m any of th e equations do you n e e d to m ultiply by a constant?
3S 2 Ch ap t er 6 Syst em s o f Eq u at i o n s an d In eq u al i t i es