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:
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Multiply the second equation by 3 to make the coefficients of y in both equations equal: 3(3x - y) = 3(30) 9x - 3y = 90
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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
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Solve for x: x = 89 / 7 x = 12.714
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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 one-sided 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.
When evaluating a one-sided 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.
When evaluating a one-sided 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.
When evaluating a one-sided 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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