Answer:
1. a. b = - 8
b. x = 8
c. x = 11
d. x = 5
2. 12 soccer balls and 8 basketballs can be purchased.
Step by step explanation
a. 
Calculate the sum

Collect like terms

Move variable to L.H.S and change it's sign
Similarly, Move constant to R.H.S and change its sign

Collect like terms

Change the signs on both sides of the equation

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b. 
Apply cross product property

Multiply the numbers

Move constant to R.H.S and change its sign

Calculate the difference

Divide both sides of the equation by 5

Calculate

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c. 
Apply cross product property

Multiply the numbers

Swap the sides of the equation

Move constant to R.H.S and change its sign

Calculate

Change the signs on both sides of the equation

Divide both sides of the equation by 8

Calculate

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D. 
Distribute 5 through the parentheses

Collect like terms

Swap both sides of the equation

Move constant to R.H.S and change its sign

Calculate the sum

Divide both sides of the equation by 11

Calculate

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2.
Solution,
No.of students in soccer = x
No.of students in basketball = y
Total no.of students = 20
i.e x + y = 20 → equation ( i )
Cost of soccer ball = $ 7
Cost of basketball = $ 10
Total budget = $ 164
i.e 7x + 10 y = 165 → equation ( ii )
In equation ( i ),
x + y = 20
Move 'y' to R.H.S and change its sign
x = 20 - y
Put the value of x in equation ( i )






Now, put the value of y in equation ( i ) ,
x + y = 20



Hence, 12 soccer balls and 8 basketballs can be purchased.
Hope this helps...
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