a Lesso n Ch eck^
Do yo u k n o w H OW?
Solve each system using substitution. Check
your solution.1. 4 y = x 2. —2x + 5y = 19
3 x - y = 70 3 x - 4 = y
Tell whether the system has one solution, infinitely
many solutions, or no solution.- y = 2x + 1
4x — 2y = 6
4. -x + 2 y= 13
x + 15 - \y - Talent Show In a talent show of singing a n d com edy
acts, singing acts are 5 m in long an d com edy acts are
3 m in long. The show has 12 acts an d lasts 50 min.
How many singing acts and how many comedy acts
are in the show?
_ MATHEMATICAL
Do y o u UN DERSTAN D? [f& j PRACTICES
6. V o c a b u l a r y W hen is th e substitution m eth o d a
b etter m e th o d th a n graphing for solving a system
of linear equations?
For each system, tell which equation you would first use
to solve for a variable in the first step of the substitution
method. Explain your choice.- —2x + y = — 1 8. 2.5x-7j/=7.5
4x + 2y = 12 6x — y = 1
Tell whether each statement is true or false. Explain.- W hen solving a system using substitution, if you obtain
an identity, th e n th e system h as no solution. - You c a n n o t u se substitution to solve a system th at does
no t have a variable w ith a coefficient of 1 or —1.
fir Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses practices
fjj Practice Solve each system using substitution. Check your answer. See Problems 1 and 2.
>Sr
11. x + y = 8 12. 2x + 2y = 38 13. x + 3 = y
y = 3x y = x + 3 3x + 4y = 7- y = 8 — x 15. y = — 2 x + 6 16. 3x + 2y = 23
t>II CMI >> 3y - x + 3 = 0 | x —4 = y
VI £?II^05 18. 4x = 3y —2 19. 2 = 2y — x
3x - 2y = 5 18 = 3x + y 23 = 5y — 4x- 4y + 3 = 3y + x 21. 7x-2y= 1 22. 4y — x = 5 + 2y
2x + 4y = 18
CM*II X 1 rH 3x + 7y = 24- Theater Tickets A dult tickets to a play cost $22. Tickets for children cost $15. See Problem 3.
Tickets for a group of 11 people cost a total of $228. W rite a n d solve a system of
equations to find how m any children a n d how m any adults w ere in th e group. - Transportation A school is p lan n in g a field trip for 142 people. The trip will use six
drivers a n d two types of vehicles: buses a n d vans. A bus can seat 51 passengers. A
van can seat 10 passengers. Write an d solve a system of eq u a tio n s to find how m any
b uses an d how m any vans will b e n eed ed. - Geom etry The m easu re of o n e acute angle in a right triangle is four tim es the
m easu re of th e o th er acute angle. W rite an d solve a system of eq u atio n s to find th e
m easures of th e acute angles.
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m 1 L e s s o n 6 - 2 S o l v i n g S y s t e m s U s i n g S u b s t i t u t i o n 3 7 5