5x + 4y = -8

6x - 4y = -80

5X + 4Y = -8 Add the 2 Eq. to

6X - 4Y = -80 eliminate y:

11X +0Y = -88
11X = -88
Divide both sides by 11:
X = -8
Substitute -8 for x in 1st Eq.
5*(-8) +4Y =- 8
Solve for Y:
-40 +4Y = -8
4Y = 32
Y = 8.
Solution set: X = -8, Y = 8.

To solve this system of equations, we can use the method of elimination. Here are the steps:

Step 1: Multiply the entire first equation by 6 and the entire second equation by 5 to eliminate the y term.

6 * (5x + 4y) = 6 * (-8)
5 * (6x - 4y) = 5 * (-80)

Step 2: Simplify the equations:

30x + 24y = -48
30x - 20y = -400

Step 3: Subtract the second equation from the first equation to eliminate the x term:

(30x + 24y) - (30x - 20y) = -48 - (-400)

Step 4: Simplify the equation:

30x + 24y - 30x + 20y = -48 + 400

Step 5: Combine like terms:

44y = 352

Step 6: Solve for y:

y = 352 / 44
y = 8

Step 7: Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:

5x + 4(8) = -8

Step 8: Simplify the equation:

5x + 32 = -8

Step 9: Subtract 32 from both sides:

5x = -8 - 32

Step 10: Simplify the equation:

5x = -40

Step 11: Divide both sides by 5 to solve for x:

x = -40 / 5
x = -8

Step 12: The solution to the system of equations is x = -8 and y = 8.

To find the solutions for this system of equations, we can use the method of elimination or substitution. Let's use the elimination method to solve this system.

First, we will manipulate the equations to eliminate one of the variables. We can do this by multiplying each equation by a suitable constant so that the coefficients of one of the variables are the same magnitude but with opposite signs.

Let's multiply the first equation by 4 and the second equation by 5 to eliminate the y variable:

4(5x + 4y) = 4(-8) becomes 20x + 16y = -32
5(6x - 4y) = 5(-80) becomes 30x - 20y = -400

Now, we can add these two equations together to eliminate the y variable:

(20x + 16y) + (30x - 20y) = -32 + (-400)
50x - 4y = -432

Next, we can rearrange this equation to solve for x:

50x = -432 + 4y
50x = 4y - 432
x = (4y - 432) / 50
x = (2y - 216) / 25

Now that we have an expression for x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:

5x + 4y = -8

Replacing x with (2y - 216) / 25:

5((2y - 216) / 25) + 4y = -8

Now, simplify the equation:

(10y - 1080) / 25 + 4y = -8

Multiply both sides by 25 to get rid of the fraction:

10y - 1080 + 100y = -200

Combine like terms:

110y - 1080 = -200

Add 1080 to both sides:

110y = 880

Divide both sides by 110:

y = 8

Now that we have the value of y, we can substitute it back into either of the original equations to solve for x. Let's use the first equation:

5x + 4y = -8

Replacing y with 8:

5x + 4(8) = -8
5x + 32 = -8

Subtract 32 from both sides:

5x = -40

Divide both sides by 5:

x = -8

Therefore, the solution to the system of equations is x = -8 and y = 8.