Algebra (FRACTIONAL COEFFICIENTS)

1/2 x + 1/3 y = 0 1/4 x - 1/2 y = 8 What is the solution of the system shown?

(-8,12)

0.01x - 0.3y = 1 y = 0.1x - 2 What is the solution of the given system?

(0.4, 2)

1/2 x + 1/3 y = 7 1/4 x + 2/3 y = 6 What is the solution of the system shown?

(10 2/3, 5)

Which of the following equations is equivalent to 1/4 x - 1/2 y = 8?

2x - 4y = 64

x - y = 2 0.2x + 0.4y = 1 The x-coordinate of the solution to the system shown is _____.

3

1/4 x + 2/3 y = 5 1/2 x + 3/2 y = 11 Which of the following expressions represents the Multiplicative Property of Equality?

3x + 8y = 60 ; x + 3y = 22

2/3 x - 1/2 y = 3 1/2 x + y = 5 Which of the following systems is equivalent to the given system?

4x - 3y = 18 and x + 2y = 10

y = 1/4 x + 7 y = 1/2 x + 5 The y-coordinate of the solution to the system shown is _____.

9

Review

A system of equations that has fractional coefficients can be rewritten so that the coefficients are integers. The multiplication property allows us to "clear fractions."

A concession-stand manager buys bottles of water and soda to sell at a football game. The manager needs to buy a total of 4,500 drinks and have 25% more water than soda. Let w be the number of bottles of water and let s be the number of bottles of soda. Create a system of equations the manager could use to find out how many bottles of water and soda to buy.

s = 4500 + w w = w = 1.25s

0.01x - 0.3y = 1 y = 0.1x - 2 Which of the following systems is equivalent to the given system?

x - 30y = 100 and 10y = x - 20