Four times a number minus twice another number is -16. The sum of the two numbers is -1. What are the numbers?
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Let's denote the first number as ( x ) and the second number as ( y ).
Given that "Four times a number minus twice another number is -16," we have the equation:
[ 4x - 2y = -16 ]
Also given that "The sum of the two numbers is -1," we have the equation:
[ x + y = -1 ]
We now have a system of two equations with two variables. We can solve this system using either substitution or elimination method.
Let's solve it using the elimination method:
From the second equation, we can express ( y ) in terms of ( x ): [ y = -1 - x ]
Now, substitute this expression for ( y ) into the first equation: [ 4x - 2(-1 - x) = -16 ]
Simplify and solve for ( x ): [ 4x + 2x - 2 = -16 ] [ 6x - 2 = -16 ] [ 6x = -14 ] [ x = -\frac{14}{6} ] [ x = -\frac{7}{3} ]
Now, substitute ( x = -\frac{7}{3} ) into the equation ( x + y = -1 ) to find ( y ): [ -\frac{7}{3} + y = -1 ] [ y = -1 + \frac{7}{3} ] [ y = -\frac{3}{3} + \frac{7}{3} ] [ y = \frac{4}{3} ]
Therefore, the first number is ( -\frac{7}{3} ) and the second number is ( \frac{4}{3} ).
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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.
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