To determine the solution to the system of equations:
-7x - 5y = 15
7x + 3y = 12
We can use the method of elimination to solve the system. By adding the two equations together, we can eliminate the variable x.
Adding the equations, we get:
(-7x - 5y) + (7x + 3y) = 15 + 12
Simplifying the equation, we have:
-2y = 27
To solve for y, we divide both sides of the equation by -2:
y = -27/2
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 second equation:
7x + 3(-27/2) = 12
Simplifying the equation, we have:
7x - 81/2 = 12
To solve for x, we can isolate it by adding 81/2 to both sides of the equation:
7x = 12 + 81/2
Combining the terms, we get:
7x = 24 + 81/2
Simplifying further:
7x = 48/2 + 81/2
7x = 129/2
Finally, we divide both sides of the equation by 7 to solve for x:
x = (129/2) / 7
x = 129/14
Therefore, the solution to the system of equations is x = 129/14 and y = -27/2.
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