6-3 and 6-4 So l v i n g Sy st e m s U si n g El i m i n a t i o n ; A p p l i c a t i o n s o f Sy st e m s
Quick Review Ex e r c i s e s
You can add or subtract equations in a system to eliminate Solve each system using elimination. Tell whether the
a variable. Before you add or subtract, you may have to system has one solution, infinitely many solutions, or
multiply one or both equations by a constant to make no solution.
eliminating a variable possible. 19. x + 2 y = 23 20. 7x + y = 6Ex a m p l e
What is the solution of the system? 3x + 2y = 415x + lOy = 5 5 5x + 3y = 34- 5x + 4 y = -8 3 22. 9x + |y=51
1
5x — 3y = 24 3x — 3y = —12 7x + |y = 39
3x + 2y = 41 Multiply by 3. 9x + 6 y = 123 23. 4x + y = 21 24. y=3x-27
5x — 3y = 24 Multiply by 2. lOx — 6 y = 48 -2 x + 6 y = 9 x — |y = 9
19x + 0 = 171
xv — Q — y 25. Flower Arranging It takes a florist 3 h 15 min to
make 3 small centerpieces and 3 large centerpieces.
3x + 2y = 41 Write the first equation. It takes 6 h 20 min to make 4 small centerpieces
3(9) + 2y = 41 Su b st i t u t e 9 for x. and 7 large centerpieces. How long does it take to
y = 7 Solve for y. make each small centerpiece and each large
centerpiece? Write and solve a system of equations
The solution is (9, 7). to find your answer.
6-5 and 6-6 Lin ear In eq u alit ies an d Syst em s of In eq u alit ies
Quick Review
A linear inequality describes a region of the coordinate
plane with a boundary line. Two or more inequalities form
a syst em o f i n eq u al i t i es. The system’s solutions lie where
the graphs of the inequalities overlap.Ex a m p l e
What is the graph of the system? y > 2x — 4
y =£ - x + 2
Graph the boundary lines
y = 2x - 4 and y = -x + 2.
For y> 2x — 4, use a dashed
boundary line and shade above
it. For y < — x + 2, use a solid
boundary line and shade below. The
green region of overlap contains the
system’s solutions.Ex e r c i se s
Solve each system of inequalities by graphing.- y>x + 4
y < 2x — 1 - 2 x - y > 0
3x+ 2y< -14 - y < lOx
y > x - 5
27. 4y < -3x
, 3
y<- 4X
29. x + 0.5y > 5.5
0.5x + y < 6.5
31. 4x + 4 > 2y
3jc - 4y > 1 - Downloads You have 60 megabytes (MB) of space
left on your portable media player. You can choose
to download song files that use 3.5 MB or video files
that use 8 MB. You want to download at least 12 files.
What is a graph showing the numbers of song and
video files you can download?
410 Chapter 6 Ch ap t er Rev i ew