Solved on Jan 25, 2024

Find two numbers whose sum is -12 and difference is -4. $x=$ $y=$

STEP 1

Assumptions
1. Let the two numbers be $x$ and $y$ .
2. The sum of the two numbers is $-12$ .
3. The difference between the two numbers is $-4$ .

STEP 2

Set up the equations based on the given information.
$x + y = -12$ $x - y = -4$

STEP 3

Solve the system of equations using the method of elimination or substitution. We will use elimination in this case.

STEP 4

Add the two equations together to eliminate $y$ .
$(x + y) + (x - y) = -12 + (-4)$

STEP 5

Simplify the left side of the equation by combining like terms.
$2x = -16$

STEP 6

Divide both sides of the equation by 2 to solve for $x$ .
$x = \frac{-16}{2}$

STEP 7

Calculate the value of $x$ .
$x = -8$

STEP 8

Now that we have the value of $x$ , we can substitute it back into one of the original equations to solve for $y$ . We will use the first equation.
$x + y = -12$

STEP 9

Substitute $x = -8$ into the equation.
$-8 + y = -12$

STEP 10

Add 8 to both sides of the equation to solve for $y$ .
$y = -12 + 8$

STEP 11

Calculate the value of $y$ .
$y = -4$
The two numbers are $x = -8$ and $y = -4$ .

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Find two numbers whose sum is -12 and difference is -4. $x=$ $y=$

STEP 1

Assumptions
1. Let the two numbers be $x$ and $y$ .
2. The sum of the two numbers is $-12$ .
3. The difference between the two numbers is $-4$ .

STEP 2

Set up the equations based on the given information.
$x + y = -12$ $x - y = -4$

STEP 3

Solve the system of equations using the method of elimination or substitution. We will use elimination in this case.

STEP 4

Add the two equations together to eliminate $y$ .
$(x + y) + (x - y) = -12 + (-4)$

STEP 5

Simplify the left side of the equation by combining like terms.
$2x = -16$

STEP 6

Divide both sides of the equation by 2 to solve for $x$ .
$x = \frac{-16}{2}$

STEP 7

Calculate the value of $x$ .
$x = -8$

STEP 8

Now that we have the value of $x$ , we can substitute it back into one of the original equations to solve for $y$ . We will use the first equation.
$x + y = -12$

STEP 9

Substitute $x = -8$ into the equation.
$-8 + y = -12$

STEP 10

Add 8 to both sides of the equation to solve for $y$ .
$y = -12 + 8$

STEP 11

Calculate the value of $y$ .
$y = -4$
The two numbers are $x = -8$ and $y = -4$ .

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Find two numbers whose sum is -12 and difference is -4. x=x=x= y=y=y=

STEP 1

Assumptions1. Let the two numbers be xxx and yyy.2. The sum of the two numbers is −12-12−12.3. The difference between the two numbers is −4-4−4.

STEP 2

Set up the equations based on the given information.x+y=−12x + y = -12x+y=−12 x−y=−4x - y = -4x−y=−4

STEP 3

Solve the system of equations using the method of elimination or substitution. We will use elimination in this case.

STEP 4

Add the two equations together to eliminate yyy.(x+y)+(x−y)=−12+(−4)(x + y) + (x - y) = -12 + (-4)(x+y)+(x−y)=−12+(−4)

STEP 5

Simplify the left side of the equation by combining like terms.2x=−162x = -162x=−16

STEP 6

Divide both sides of the equation by 2 to solve for xxx.x=−162x = \frac{-16}{2}x=2−16​

STEP 7

Calculate the value of xxx.x=−8x = -8x=−8

STEP 8

Now that we have the value of xxx, we can substitute it back into one of the original equations to solve for yyy. We will use the first equation.x+y=−12x + y = -12x+y=−12

STEP 9

Substitute x=−8x = -8x=−8 into the equation.−8+y=−12-8 + y = -12−8+y=−12

STEP 10

Add 8 to both sides of the equation to solve for yyy.y=−12+8y = -12 + 8y=−12+8

STEP 11

Calculate the value of yyy.y=−4y = -4y=−4The two numbers are x=−8x = -8x=−8 and y=−4y = -4y=−4.

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Find two numbers whose sum is -12 and difference is -4. $x=$ $y=$

Assumptions
1. Let the two numbers be $x$ and $y$ .
2. The sum of the two numbers is $-12$ .
3. The difference between the two numbers is $-4$ .

Set up the equations based on the given information.
$x + y = -12$ $x - y = -4$

Add the two equations together to eliminate $y$ .
$(x + y) + (x - y) = -12 + (-4)$

Simplify the left side of the equation by combining like terms.
$2x = -16$

Divide both sides of the equation by 2 to solve for $x$ .
$x = \frac{-16}{2}$

Calculate the value of $x$ .
$x = -8$

Now that we have the value of $x$ , we can substitute it back into one of the original equations to solve for $y$ . We will use the first equation.
$x + y = -12$

Substitute $x = -8$ into the equation.
$-8 + y = -12$

Add 8 to both sides of the equation to solve for $y$ .
$y = -12 + 8$

Calculate the value of $y$ .
$y = -4$
The two numbers are $x = -8$ and $y = -4$ .