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How do you solve the system of equations #2x+8y=6# and #-5x-20y=-15#?

Answer 1

This system of equation doesn't have any solutions.

#2x+8y=6# #-5x-20y=-15#

Let's simplify these equations: divide the first one by #2# andd the second by #-5#:

#x+4y=3# #x+4y=15#

Now, using any of the equations, we must express one variable by the other, let's say #x# by #y# from the second equation:

#x=15-4y#

Using this we solve the other equation:

#x+4y=3# #15-4y+4y=3# #15=3#

We got #15=3# which obviously isn't true so this equation has no solution. It follows that this system of equation doesn't have any solutions as well.

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Answer 2

Nathan Axel

#x# can have any value and the equations will work.
The y- values will depend on the x chosen.

#2x+8y =6" and "-5x -20y = -15#

There are different options available to solve the equations. #rarr" "# elimination #rarr" "# substitution #rarr# single variable #rarr" "# equating #rarr" "#matrices #rarr" "# graphically

To be able to use substitution, a single variable in one of the equations is a useful indicator

#2x+8y =6 " "div2 rarr " "x+4y=3#

Make x the subject of the equation:

#color(red)(x = 3-4y)#

Replace #color(red)x# in the second equation by #color(red)((3-4y))#

#" "-5color(red)(x) -20y = -15# #color(white)(xxxx)darr# #-5color(red)((3-4y))-20y =-15#

#-15+20y -20y = -15#

#-15 = -15#

#x# can have any value

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Answer 3

Eva Abramson

To solve the system of equations 2x + 8y = 6 and -5x - 20y = -15, you can use the method of substitution or elimination. Let's use elimination:

Multiply the first equation by 5 and the second equation by 2 to make the coefficients of x in both equations equal:

Equation 1: 10x + 40y = 30 Equation 2: -10x - 40y = -30
Add the two equations together to eliminate the variable x:

(10x + 40y) + (-10x - 40y) = 30 + (-30) 0 = 0
Since 0 = 0 is always true, it means the system is consistent and dependent.
There are infinitely many solutions. The solutions can be expressed as:

x = any real number y = (6 - 2x) / 8

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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.