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How do you solve the following system?: # x - y = -6, x+y=4 #

Answer 1

Avery Alexander

The solution for the system of equations is
#color(blue)(x=-1,y=5#

#xcolor(blue)(-y)=-6#......equation #1# #x+color(blue)(y)=4#...........equation #2#

Adding the two equations results in elimination of #color(blue)(y#

#xcancelcolor(blue)(-y)=-6# #x+cancelcolor(blue)(y)=4#

#2x=-2#

#x=(-2)/2#

#color(blue)(x=-1#

Finding #y# from equation #1# #x+y=4#

#y=4-x#

#y=4-(-1)#

#y=4+1#

#color(blue)(y=5#

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Answer 2

Nathan Axel

To solve the system of equations ( x - y = -6 ) and ( x + y = 4 ), we can use the method of addition or elimination:

Add the two equations: [ (x - y) + (x + y) = -6 + 4 ] [ 2x = -2 ]
Solve for x: [ x = -1 ]
Substitute x = -1 into one of the original equations to solve for y. Let's use the second equation: [ -1 + y = 4 ] [ y = 5 ]

So the solution to the system is ( x = -1 ) and ( y = 5 ).

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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.