Final answer:
The solution to the system of equations -5x - 5y = -30 and 10x + 3y = -3 is found by using the elimination method, resulting in x = -3 and y = 9.
Step-by-step explanation:
To solve the system of equations -5x - 5y = -30 and 10x + 3y = -3, we can use the method of substitution or elimination. Here, let's use the elimination method.
First, we simplify the first equation by dividing every term by -5 to make the coefficients of one of the variables (y in this case) the same:
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- (-5x - 5y) / -5 = -30 / -5
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- x + y = 6
Next, we multiply the newly obtained equation by -3 to get the coefficients of y in the second equation to match:
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- -3(x + y) = -3(6)
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- -3x - 3y = -18
Now we can add the second original equation 10x + 3y = -3 to the equation we just derived:
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- (-3x - 3y) + (10x + 3y) = -18 + (-3)
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- 7x = -21
Dividing both sides by 7 gives us the value of x:
Now we substitute x into x + y = 6 to find y:
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- (-3) + y = 6
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- y = 6 + 3
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- y = 9
The solution to the system is x = -3 and y = 9.