Four times a number minus twice another number is -16. The sum of the two numbers is -1. What are the numbers?

Answer 1

#-3" and "2#

#"let the 2 numbers be "x" and "y#
#"we can set up 2 equations to model the statements"#
#4x-2y=-16to(1)#
#x+y=-1to(2)#
#"multiply equation "(2)" by 2"#
#rArr2x+2y=-2to(3)#
#"adding equations "(1)" and "(3)" will eliminate y"#
#(4x+2x)+cancel(-2y+2y)^0=(-16-2)#
#rArr6x=-18#
#"divide both sides by 6"#
#(cancel(6) x)/cancel(6)=(-18)/6#
#rArrx=-3#
#"substitute "x=-3" into equation "(2)#
#-3+y=-1#
#rArry=-1+3=2#
#"the numbers are "-3" and "2#
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Answer 2

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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Answer from HIX Tutor

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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