I am great at math but for some reason can not wrap my brain around Algebra for the world! Please Help!! Im stumped!

Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.

-3x – 5y = 61

7x – 5y = -9

-3x-5y=61 (1)

7x-5y=-9 (2)
Looking at the equations, we can multiply either of them by -1 to cancel the y's. Let's do that to the 2nd one.
-3x-5y=61
-7x+5y=9
Then add the equations together.
-10x=70
x=-7
Plug that back into either original equation to solve for y.

use the elimination method to solve the system of equations choose the correct ordered pair 6x+5y=61-5x+5y=-5

To solve the system of equations using the elimination method, we need to eliminate one of the variables by multiplying one or both of the equations by a suitable constant. This will allow us to add or subtract the resulting equations and eliminate one variable.

In this case, we can eliminate the variable "y" by multiplying the first equation by 5 and the second equation by -1. Let's first rewrite the equations with the adjustment:

-3x – 5y = 61 -> multiplying by 5 -> -15x - 25y = 305
7x – 5y = -9 -> multiplying by -1 -> -7x + 5y = 9

Now, let's add the two equations together:

(-15x - 25y) + (-7x + 5y) = 305 + 9

Simplifying the equation:

-15x - 25y - 7x + 5y = 314
-22x - 20y = 314

Now, we have a new equation:

-22x - 20y = 314

To continue solving, we can choose either variable to eliminate. Let's eliminate "y" using the second equation:

-7x + 5y = 9

To do this, we need to multiply the equation by 4:

4(-7x + 5y) = 4(9)
-28x + 20y = 36

Now, let's add the new equation with -22x - 20y = 314:

(-22x - 20y) + (-28x + 20y) = 314 + 36

Simplifying the equation:

-22x - 20y - 28x + 20y = 350
-50x = 350

Dividing both sides by -50:

x = -7

Now that we have the value of x, we can substitute it into one of the original equations to find the value of y. Let's use the second equation:

7x - 5y = -9

Substituting x = -7:

7(-7) - 5y = -9
-49 - 5y = -9

Simplifying the equation:

-5y = 40

Dividing both sides by -5:

y = -8

Therefore, the solution to the system of equations is x = -7 and y = -8.

The elimination method allows us to subtract or add multiples of the equations to eliminate a variable. By systematically manipulating the equations, we can solve for the unknown variables.