# solve the system by addition:

-5x-9y = -5
x+5y=-15

I've tried this one over and over, but I can't seem to get the right answer. I don't even really know where to start. each time i try to do it, i go about it a little differently and i'm completely lost, pls help!!

from the second equation:
x=-5y-15
now sub that back in the first one:
-5(-5y-15)-9y=-5
25y+75-9y=-5
16y=-5-75
16y=-80
y=-5
now sub that back into x=-5y-15
x=-5(-5)-15
x=25-15
x=10

OR
first equation .....
-5x - 9y = -5
second equation times 5 ...
5x + 25y = -75

add them, the x's are eliminated

16y = -80
y = -5
substitute that in one of the originals, etc

## Ah, the joy of solving systems of equations. It can be quite the puzzle, can't it? But fear not, my friend, for Clown Bot is here to help with a touch of humor!

Let's tackle this system together. We'll start by using the addition method, also known as the elimination method. So, we have the equations:

-5x - 9y = -5 ...(1)
x + 5y = -15 ...(2)

To eliminate the variable "x," we need to make the coefficients of "x" in both equations equal. To do that, we can multiply equation (2) by 5:

5(x + 5y) = 5(-15)
5x + 25y = -75 ...(3)

Now, we can add equations (1) and (3) to eliminate "x":

(-5x - 9y) + (5x + 25y) = -5 + (-75)
-5x + 5x - 9y + 25y = -5 - 75
16y = -80

Ah, the variable "x" disappears like a magician's rabbit! Now, let's solve for "y" by dividing both sides by 16:

16y/16 = -80/16
y = -5

Wonderful! We've found the value of "y." Now, let's substitute it back into equation (2) to find "x":

x + 5(-5) = -15
x - 25 = -15
x = 10

Voila! We've discovered that "x" is equal to 10 and "y" is equal to -5. And just like that, we've solved the system using the addition method!

Remember, my friend, math may sometimes be a bit tricky, but don't let it get you down. With a dash of humor and perseverance, you can conquer any equation!

## To solve the system of equations by addition, follow these steps:

Step 1: Write the system of equations:
-5x - 9y = -5 ...(Equation 1)
x + 5y = -15 ...(Equation 2)

Step 2: Multiply Equation 2 by 5 to eliminate the x terms:
5(x + 5y) = 5(-15)
5x + 25y = -75 ...(Equation 3)

Step 3: Add Equation 1 and Equation 3 together:
-5x - 9y + 5x + 25y = -5 - 75
(5x - 5x) + (-9y + 25y) = -80
16y = -80

Step 4: Solve for y:
Divide both sides of the equation by 16:
16y/16 = -80/16
y = -5

Step 5: Substitute the value of y into either Equation 1 or Equation 2 to solve for x. Let's use Equation 2:
x + 5(-5) = -15
x - 25 = -15
x = -15 + 25
x = 10

So, the solution to the system of equations is x = 10 and y = -5.

## To solve the system of equations by addition, we need to eliminate one variable by adding the two equations together. Let's go through the steps in a more organized manner:

-5x - 9y = -5
x + 5y = -15

2. We can eliminate the variable x by multiplying the second equation by 5. This will give us the same coefficient for x in both equations, but with opposite signs:
-5x - 9y = -5
5x + 25y = -75

3. Now we can add the two equations together to eliminate x:
(-5x - 9y) + (5x + 25y) = -5 + (-75)
-5x + 5x - 9y + 25y = -5 - 75
16y = -80

4. Simplify the equation:
16y = -80

5. Solve for y by dividing both sides of the equation by 16:
y = -80 / 16
y = -5

6. Substitute the value of y back into one of the original equations to solve for x. Let's use the second equation:
x + 5y = -15
x + 5(-5) = -15
x - 25 = -15
x = -15 + 25
x = 10

Therefore, the solution to the system of equations is x = 10 and y = -5.

Make sure to double-check your work by substituting the values of x and y back into both equations to ensure they satisfy both equations.