Please help solve with elimination method.

-6x+6y=18
7x+5y=-9

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X= 0.5

Y= 2.5

To solve this system of equations using the elimination method, we need to eliminate one of the variables by multiplying one of the equations by a constant so that when added to the other equation, one of the variables will cancel out.

Let's start by multiplying the two equations by the necessary constants to eliminate one of the variables.

To eliminate the x variable, we need to multiply the first equation by 7 and the second equation by 6. This will give us:

7(-6x + 6y) = 7(18)
6(7x + 5y) = 6(-9)

Simplifying these equations, we get:

-42x + 42y = 126
42x + 30y = -54

Now, let's add these two equations together:

(-42x + 42y) + (42x + 30y) = 126 + (-54)

When we combine like terms, the x variable cancels out:

42y + 42y + 30y = 126 - 54
114y = 72

Divide both sides of the equation by 114 to solve for y:

y = 72/114
y = 0.63

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

-6x + 6(0.63) = 18

Simplifying, we get:

-6x + 3.78 = 18

To isolate the x variable, subtract 3.78 from both sides:

-6x = 18 - 3.78
-6x = 14.22

Divide both sides of the equation by -6 to solve for x:

x = 14.22 / -6
x = -2.37

Therefore, the solution to the system of equations is x = -2.37 and y = 0.63.