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(3x + 3y = -21
(x + y = -7
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User Bbrown
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1 Answer

1 vote

Answer: x= -8 and y= 1

Explanation:

First, let's work on your first equation,3x+3y=-21

This means, see if it can be simplified at all before attempting to solve it.

Multiply x and 3

Multiply x and 1

The x just gets copied along.

The answer is x

x

3*x evaluates to 3x

Multiply y and 3

Multiply y and 1

The y just gets copied along.

The answer is y

y

3*y evaluates to 3y

3*x+3*y evaluates to 3x+3y

Because of the minus sign

21 becomes - 21

The answer is -21

So, all-in-all, your first equation can be written as: 3x+3y = -21

Now, let's work on your second equation,x+y=-7 x+y evaluates to x+y

Because of the minus sign

7 becomes - 7

The answer is -7

So, all-in-all, your second equation can be written as: x+y = -7

After this initial survey of the equations, the system of equations we'll set out to solve is:

3x+3y = -21 and x+y = -7

Let's start by solving 3x+3y = -21 for the variable x.

Move the 3y to the right hand side by subtracting 3y from both sides, like this:

From the left hand side:

3y - 3y = 0

The answer is 3x

From the right hand side:

The answer is -21-3y

Now, the equation reads:

3x = -21-3y

To isolate the x, we have to divide both sides of the equation by the other variables

around the x on the left side of the equation.

The last step is to divide both sides of the equation by 3 like this:

To divide x by 1

The x just gets copied along in the numerator.

The answer is x

3x ÷ 3 = x

To divide -21-3y by 3

divide each term in -21-3y by 3 term by term.

-21 ÷ 3 = -7

To divide y by 1

The y just gets copied along in the numerator.

The answer is y

-3y ÷ 3 = -y

The solution to your equation is:

x = -7-y

Next, let's solve x+y = -7 for the variable y.

Move the x to the right hand side by subtracting x from both sides, like this:

From the left hand side:

x - x = 0

The answer is y

From the right hand side:

The answer is -7-x

Now, the equation reads:

y = -7-x

To isolate the y, we have to divide both sides of the equation by the other variables

around the y on the left side of the equation.

and this is the final solution to your equation.

Now, plug the earlier result, x=-7-y, in for x everywhere it occurs in

y=-7-x.

This gives y=-7-(-7-y). Now all we have to do is solve this for y,to have our first solution.

Because of the minus sign

7 becomes - 7

The answer is -7

Because of the minus sign

7 becomes - 7

The answer is -7

-7-y evaluates to -7-y

-7 - -7 = 0

The answer is y

-7-(-7-y) evaluates to y

Move the y to the left hand side by subtracting y from both sides, like this:

From the left hand side:

y - y = 0

The answer is 0

From the right hand side:

y - y = 0

The answer is 0

Now, the equation reads:

0 = 0

To isolate the y, we have to divide both sides of the equation by the other variables

around the y on the left side of the equation.

The last step is to divide both sides of the equation by 0 like this:

Sorry, can't divide by zero! Stop! Everything below this line is wrong.

0 ÷ 0 = 1

Sorry, can't divide by zero! Stop! Everything below this line is wrong.

0 ÷ 0 = 1

The solution to your equation is:

1 = 1

Lastly, to find the solution for x, we plug this answer for y into the earlier result that

x=-7-y.

This gives x=-7-(1). Now, simplify this.

Because of the minus sign

7 becomes - 7

The answer is -7

-7-(1) evaluates to -8

x= -8

User Mukhammad Ali
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