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Mr. Sims
Solve by using the substitution method.
1. x + y = 8
Algebra 1
Section 7.9 B
Cumulative Review #2
x = -y + 8
-y -y
2x + y = 10
get one of the equations
to read x = or y =
2(-y + 8) + y = 10
-2y + 16 + y = 10
-y + 16 = 10
-16
distributive property
-16
-y = -6
y=6
substitute 6 for y
into equation x = -y + 8
x = -y + 8
x = -6 + 8
x=2
Mr. Sims
Solve by using the addition method.
1
xy7
4
2.
-x + 4y = -28
4
x + 4y = 0
x  4y  0
multiply by a term to cancel
out a variable when added
8y = -28
28
y
8
7
y
2
x + 4y = 0
2  7
x  4    0
 2
x – 14 = 0
substitute –7/2 for y
into any equation
+14 +14
x = 14
Mr. Sims
Simplify the expression.
 1 
3.  2 
x 
1
 14
x
5.
7
power to a power
- multiply exponents
8
x
4.
x10
1
 2
x
cancel
4
(2x) 3
= 4(2x)3
move 2x up to make
a positive exponent
= 4(8x3)
take everything in parentheses
to the 3rd power
= 32x3
Mr. Sims
Simplify the expression.
3
6.   8x


5 
 4xy 
4
6 x4
64x

16x 2 y10
4x 4
 10
y
2
take everything in parentheses
to the 2nd power
cancel {subtract exponents
when dividing}
7. 5x  (x  x 4 ) 2
3 2 work in parentheses 1st
 5x(x ) {add exponents when multiplying}
 5x(x 6 )
 5x 5
5
 5
x
power to a power
multiply exponents
add exponents when multiplying
move into denominator to make
positive exponent
Mr. Sims
8.
3 2 1 3 
2
(6a )  a 
2 
1 
everything in parentheses
 36a 6  a 6  take
 4  to exponents on outside
{power to a power: multiply exponents}
= 9a12
add exponents when multiplying
9. (r2st5)0(s4t2)3
=
take everything in parentheses
12
6
s t
to exponent on outside
{anything to zero power is 1}
Mr. Sims
10.
6x 4 y 4 5x 2 y3

3xy
2y 2
5x5y4 6 7
30x y

6xy3
multiply across (horizontally)
1
= 5x5y4
cancel
Mr. Sims
Evaluate the expression. (Write result in decimal form)
11. (5 × 10 –2) · (3 × 10 4)
= 15 × 102 add exponents when multiplying
= 1500
12. (6 × 10 – 4) · (7 × 10 –5)
= 42 × 10 –9 add exponents when multiplying
= .000000042
13. (20 × 10 – 4)  (2.5 × 10 –8)
= 8 × 10 4 subtract exponents when dividing
= 80,000
14. (8.8 × 10 –1) (11 × 10 –1)
= .8 × 100 subtract exponents when dividing
= .8 anything to zero power is 1
Mr. Sims
Use substitution to solve the system of equations.
1.) 5g + 4h = -9
g–h=0
Algebra 1
Sect. 7.9 B
Assignment
2.) 3.4x + 5.9y = 3.1
x + .1y = 1
Use the addition method to solve the system of equations.
3.) 6r + 3s = -1
-6r + 4s = 9
4.) 10x + 16y = 140
5x – 8y = 60
Mr. Sims
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Mr. Sims