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:
1. Start with the two equations:
-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.