Understanding Linear Equations

Solve the system of equations: 2x + 3y = 12 and x - y = 1.

• (3, 2)

• (4, 0)

• (1, 4)

• (2, 3)

What is the solution to the equations: 3x + 4y = 24 and 2x - y = 3?

• (36/11, 39/11)

• (12, 6)

• (0, 0)

• (5, 5)

Using substitution, solve for y in the equations: y = 2x + 1 and 3x + 2y = 12.

• y = 27/7

• y = 3x + 2

• y = 4x + 3

• y = 5x - 1

Apply the elimination method to find x and y in: 4x + 5y = 20 and 2x - 3y = 6.

• x = 10, y = 0

• x = 45/11, y = 8/11

• x = 5, y = 2

• x = 0, y = 4

If x + y = 10 and x - y = 2, what are the values of x and y?

• x = 6, y = 4

• x = 4, y = 6

• x = 8, y = 2

• x = 5, y = 5

A store sells pencils for $0.50 each and erasers for $0.75 each. If you buy 10 items for $6.00, how many of each did you buy?

• 5 pencils and 5 erasers

• 7 pencils and 3 erasers

• 4 pencils and 6 erasers

• 6 pencils and 4 erasers

Solve the following system using substitution: y = 3x - 4 and 2x + y = 10.

• (5, 5)

• (14/5, 22/5)

• (2, 2)

• (0, 10)

Using elimination, find the values of x and y in: 5x + 2y = 30 and 3x + 4y = 24.

• x = 6, y = 3

• x = 4, y = 8

• x = 2, y = 10

• x = 5.14, y = 2.15

If the sum of two numbers is 15 and their difference is 3, what are the two numbers?

• 8 and 7

• 10 and 5

• 12 and 3

• The two numbers are 9 and 6.

A farmer has chickens and cows. If he has 20 animals in total and there are 56 legs, how many chickens and cows does he have?

• 12 chickens and 8 cows

• 8 chickens and 12 cows

• 10 chickens and 10 cows

• 14 chickens and 6 cows