Real-World Applications Systems of Equations

What are the two equations given the following statement: The sum of two numbers is 24 and their difference is 2.

• $x+y=24,\ \frac{x}{y}=2$

• $x-y=24,\ x+y=2$

• $x+y=24,\ x-y=2$

• $x\times y=24,\ \frac{x}{y}=2$

What are the two equations based on the statement: The sum of two numbers is 36. Twice the first number minus the second is 6.

• $x+y=36,\ 2y+x=6$

• $x+y=36,\ 2x-y=6$

• $2x+y=36,\ x+y=6$

• $x+y=6,\ 2x-y=36$

Write the equations for the following statement: The sum of two numbers is 25. One number is twice the second number plus 7.

• $x-y=7,\ x=2y+7$

• $x-y=25,\ x=2y-7$

• $x+y=7,\ y=2x-25$

• $x+y=25,\ x=2y+7$

Identify the variables in the following problem: The cost of 12 oranges and 7 apples is $5.36. 8 oranges and 5 apples cost $3.68.

• x = oranges, y = apples

• x = total cost in trip 1, y = total cost in trip 2

• x = total cost of oranges, y = total cost of apples

Identify the variables in the following problem: At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $43. Tori bought two pairs of gloves and two hats for $30.

• x = cody, y = tori

• x = gloves, y = hats

• x = people, y = items

Solve the following systems of equations:

 $2x+2y=28$  , $8y-2y=22$  

• (9,5)

• (5,9)

• (2,10)

• (10,2)

Solve the following systems of equations:

 $y=7x+6$  , $4x-3y=16$  

• (-2,-8)

• (-8,-2)

• (2,10)

• (10,2)

What would the two equations be from the following problem: Cody bought 2 pairs of gloves and 4 hats for $43. Tori bought 2 pairs of gloves and 2 hats for $30.

• 2x+4y=43, 2x-2y=30

• 2x-4y=30, 2x+2y=43

• 2x+2y=43, 2x+2y=30

• 2x+4y=30, 2x+2y=43

What would the two equations be from the following problem: The cost of 12 oranges and 7 apples is $5.36. The cost of 8 oranges and 5 apples is $3.68.

• 12x+7y=3.68, 8x+5y=5.36

• 12x-7y=5.36, 8x-5y=3.68

• 12x+7y=5.36, 8x+5y=3.68

• 12x-7y=3.68, 8x-5y=5.36

solve for x and y: Cody bought 2 pairs of gloves and 4 hats for $43. Tori bought 2 pairs of gloves and 2 hats for $30.

• (17,13)

• (13,17)

• $\left(8.50,6.50\right)$

• $\left(-8.50,-6.50\right)$