Question

Write the equations: Jack and his sister Malonie are 4 years apart in age. The sum of their ages is 28. What are their ages?
Let _x_ = ___x - y = 4___
Let _y_=___x + y = 2___

Answer 1

Write the equations: The difference of two numbers is 3 and their sum is 13. What are the two numbers?
Let _x_ = __x - y = 3__
Let _y_=__x + y = 13__

Answer 2

Write the equations: The difference of two numbers is -10 and the sum is -4.
Let _x__ = __x - y = -10__
Let _y__=__x + y = -4__

Answer 3

Write the equations: Two of Julie’s textbooks are a total of $65. The difference in price between the two books is $9. What is the cost of each book?
Let _x _ = ___x + y = 65___
Let _y__=__x - y = 9__

Answer 4

Write a system of equations where the sum of two numbers is 10 and the difference is 6. Can you determine the solution without graphing? Guess and check.

Answer 5

Let x = Jack's age
Let y = Malonie's age

From the given information, we can write the following equations:

1) x - y = 4 (Jack's age minus Malonie's age is 4 years)
2) x + y = 28 (The sum of their ages is 28)

Simplifying equation 1:

x = y + 4

Substituting this value of x into equation 2:

y + 4 + y = 28
2y + 4 = 28
2y = 24
y = 12

Substituting this value of y back into equation 1:

x - 12 = 4
x = 16

Therefore, Jack is 16 years old and Malonie is 12 years old.

Answer 6

Let x = first number
Let y = second number

From the given information, we can write the following equations:

1) x - y = 3 (The difference of the two numbers is 3)
2) x + y = 13 (The sum of the two numbers is 13)

Simplifying equation 1:

x = y + 3

Substituting this value of x into equation 2:

y + 3 + y = 13
2y + 3 = 13
2y = 10
y = 5

Substituting this value of y back into equation 1:

x - 5 = 3
x = 8

Therefore, the two numbers are 8 and 5.

Answer 7

Let x = first number
Let y = second number

From the given information, we can write the following equations:

1) x - y = -10 (The difference of the two numbers is -10)
2) x + y = -4 (The sum of the two numbers is -4)

Simplifying equation 1:

x = y - 10

Substituting this value of x into equation 2:

y - 10 + y = -4
2y - 10 = -4
2y = 6
y = 3

Substituting this value of y back into equation 1:

x - 3 = -10
x = -7

Therefore, the two numbers are -7 and 3.

Answer 8

Let x = price of the first book
Let y = price of the second book

From the given information, we can write the following equations:

1) x + y = 65 (The sum of the prices of the two books is $65)
2) x - y = 9 (The difference in price between the two books is $9)

To solve this system of equations, we can add equations 1 and 2:

(x + y) + (x - y) = 65 + 9
2x = 74
x = 37

Substituting this value of x into equation 1:

37 + y = 65
y = 65 - 37
y = 28

Therefore, the cost of the first book is $37 and the cost of the second book is $28.

Answer 9

Let x = first number
Let y = second number

From the given information, we can write the following equations:

1) x + y = 10 (The sum of the two numbers is 10)
2) x - y = 6 (The difference between the two numbers is 6)

To determine the solution without graphing, we can use guess and check method:

Let's start with assuming x = 8 and y = 2:

1) 8 + 2 = 10 (satisfies the first equation)
2) 8 - 2 = 6 (satisfies the second equation)

Therefore, when x = 8 and y = 2, the sum of the two numbers is 10 and the difference is 6.

So the solution to the system of equations is x = 8 and y = 2.