Math / Algebra

QuestionStory Problem The sum of two numbers is -22 . The difference of the two numbers is 8 . What are the two numbers?
Let Statements $=-7$ $=-15$ Rewrite the system so like terms are aligned.
Multiply, if necessary, to make elimination possible.
Determine which variable you will elliminate. $y$ Combine the equations and solve for the other variable.
Substitute to solve for the Write the solution. eliminated variable.

Studdy Solution

STEP 1

What is this asking? We need to find two mystery numbers that add up to -22 and have a difference of 8! Watch out! Don't mix up the sum and the difference!
Also, be careful with those negative signs; they can be sneaky.

STEP 2

1. Set up the system of equations
2. Eliminate a variable
3. Solve for the first number
4. Solve for the second number

STEP 3

Let's call our two mystery numbers $x$ and $y$ .
We know that when we add them together, we get -22.
So, we can write that as an equation: $x + y = -22$

STEP 4

We also know that the difference between the two numbers is 8.
Let's write that as another equation: $x - y = 8$

STEP 5

Now, look at our two equations.
Notice how one has $+y$ and the other has $-y$ ?
Perfect! We can add the two equations together, and the $y$ terms will add to zero, effectively eliminating $y$ !

STEP 6

Let's do it! $(x + y) + (x - y) = -22 + 8$ $2x = -14$

STEP 7

We're so close!
We have $2x = -14$ .
To get $x$ by itself, we need to divide both sides of the equation by 2: $\frac{2x}{2} = \frac{-14}{2}$ $x = -7$ Woohoo! We found our first mystery number: $x = \mathbf{-7}$ !

STEP 8

Now, let's use the value of $x$ to find $y$ .
We can use either of our original equations.
Let's use the first one: $x + y = -22$ .

STEP 9

We know $x = -7$ , so we can substitute that in: $-7 + y = -22$

STEP 10

To get $y$ by itself, we need to add 7 to both sides of the equation: $-7 + y + 7 = -22 + 7$ $y = -15$ Yes! Our second mystery number is $y = \mathbf{-15}$ !

STEP 11

The two numbers are $\mathbf{-7}$ and $\mathbf{-15}$ !

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Studdy Solution

STEP 1

What is this asking? We need to find two mystery numbers that add up to -22 and have a difference of 8! Watch out! Don't mix up the sum and the difference!
Also, be careful with those negative signs; they can be sneaky.

STEP 2

1. Set up the system of equations
2. Eliminate a variable
3. Solve for the first number
4. Solve for the second number

STEP 3

Let's call our two mystery numbers $x$ and $y$ .
We know that when we add them together, we get -22.
So, we can write that as an equation: $x + y = -22$

STEP 4

We also know that the difference between the two numbers is 8.
Let's write that as another equation: $x - y = 8$

STEP 5

Now, look at our two equations.
Notice how one has $+y$ and the other has $-y$ ?
Perfect! We can add the two equations together, and the $y$ terms will add to zero, effectively eliminating $y$ !

STEP 6

Let's do it! $(x + y) + (x - y) = -22 + 8$ $2x = -14$

STEP 7

We're so close!
We have $2x = -14$ .
To get $x$ by itself, we need to divide both sides of the equation by 2: $\frac{2x}{2} = \frac{-14}{2}$ $x = -7$ Woohoo! We found our first mystery number: $x = \mathbf{-7}$ !

STEP 8

Now, let's use the value of $x$ to find $y$ .
We can use either of our original equations.
Let's use the first one: $x + y = -22$ .

STEP 9

We know $x = -7$ , so we can substitute that in: $-7 + y = -22$

STEP 10

To get $y$ by itself, we need to add 7 to both sides of the equation: $-7 + y + 7 = -22 + 7$ $y = -15$ Yes! Our second mystery number is $y = \mathbf{-15}$ !

STEP 11

The two numbers are $\mathbf{-7}$ and $\mathbf{-15}$ !

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Studdy Solution

STEP 1

What is this asking? We need to find two mystery numbers that add up to -22 and have a difference of 8! Watch out! Don't mix up the sum and the difference!Also, be careful with those negative signs; they can be sneaky.

STEP 2

1. Set up the system of equations2. Eliminate a variable3. Solve for the first number4. Solve for the second number

STEP 3

Let's call our two mystery numbers xxx and yyy.We know that when we add them together, we get -22.So, we can write that as an equation: x+y=−22 x + y = -22 x+y=−22

STEP 4

We also know that the difference between the two numbers is 8.Let's write that as another equation: x−y=8 x - y = 8 x−y=8

STEP 5

Now, look at our two equations.Notice how one has +y+y+y and the other has −y-y−y?Perfect! We can **add** the two equations together, and the yyy terms will add to zero, effectively eliminating yyy!

STEP 6

Let's do it! (x+y)+(x−y)=−22+8 (x + y) + (x - y) = -22 + 8 (x+y)+(x−y)=−22+8 2x=−14 2x = -14 2x=−14

STEP 7

We're so close!We have 2x=−142x = -142x=−14.To get xxx by itself, we need to divide both sides of the equation by **2**: 2x2=−142 \frac{2x}{2} = \frac{-14}{2} 22x​=2−14​ x=−7 x = -7 x=−7Woohoo! We found our first mystery number: x=−7x = \mathbf{-7}x=−7!

STEP 8

Now, let's use the value of xxx to find yyy.We can use either of our original equations.Let's use the first one: x+y=−22x + y = -22x+y=−22.

STEP 9

We know x=−7x = -7x=−7, so we can substitute that in: −7+y=−22 -7 + y = -22 −7+y=−22

STEP 10

To get yyy by itself, we need to add **7** to both sides of the equation: −7+y+7=−22+7 -7 + y + 7 = -22 + 7 −7+y+7=−22+7 y=−15 y = -15 y=−15Yes! Our second mystery number is y=−15y = \mathbf{-15}y=−15!

STEP 11

The two numbers are −7\mathbf{-7}−7 and −15\mathbf{-15}−15!

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to find two mystery numbers that add up to -22 and have a difference of 8! Watch out! Don't mix up the sum and the difference!
Also, be careful with those negative signs; they can be sneaky.

1. Set up the system of equations
2. Eliminate a variable
3. Solve for the first number
4. Solve for the second number

Let's call our two mystery numbers $x$ and $y$ .
We know that when we add them together, we get -22.
So, we can write that as an equation: $x + y = -22$

We also know that the difference between the two numbers is 8.
Let's write that as another equation: $x - y = 8$

Now, look at our two equations.
Notice how one has $+y$ and the other has $-y$ ?
Perfect! We can add the two equations together, and the $y$ terms will add to zero, effectively eliminating $y$ !

Let's do it! $(x + y) + (x - y) = -22 + 8$ $2x = -14$

We're so close!
We have $2x = -14$ .
To get $x$ by itself, we need to divide both sides of the equation by 2: $\frac{2x}{2} = \frac{-14}{2}$ $x = -7$ Woohoo! We found our first mystery number: $x = \mathbf{-7}$ !

Now, let's use the value of $x$ to find $y$ .
We can use either of our original equations.
Let's use the first one: $x + y = -22$ .

We know $x = -7$ , so we can substitute that in: $-7 + y = -22$

To get $y$ by itself, we need to add 7 to both sides of the equation: $-7 + y + 7 = -22 + 7$ $y = -15$ Yes! Our second mystery number is $y = \mathbf{-15}$ !

The two numbers are $\mathbf{-7}$ and $\mathbf{-15}$ !