How do you solve the following system?: # 2x + 3y = 1 , 3x − y = 30 #
Arrange equations.
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To solve the system of equations:
2x + 3y = 1
3x  y = 30
You can use the method of substitution or elimination. Here's the solution using the elimination method:

Multiply the second equation by 3 to make the coefficients of y in both equations equal: 3(3x  y) = 3(30) 9x  3y = 90

Now, subtract the first equation from the modified second equation to eliminate y: (9x  3y)  (2x + 3y) = 90  1 9x  3y  2x  3y = 89 7x = 89

Solve for x: x = 89 / 7 x = 12.714

Substitute the value of x into one of the original equations to find y. Let's use the first equation: 2(12.714) + 3y = 1 25.428 + 3y = 1 3y = 1  25.428 3y = 24.428 y = 24.428 / 3 y = 8.143
So, the solution to the system of equations is x ≈ 12.714 and y ≈ 8.143.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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