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How do you solve the following system: #3x+y=8, 2x-y=7 #?

Answer 1

Hazel Anglin

#x=3#
#y=-1#

Given -

#3x+y=8# ------------- (1) #2x-y=7# ---------------(2) -----#(1) + (2)#

#5x=15#

#x=15/5=3#

#x=3#

Substitute >#x=3# in equation (1)

#3(3)+y=8#

#9+y=8#

#y=8-9=-1#

#y=-1#

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Answer 2

Hazel Anglin

To solve the system of equations:

Begin by solving one equation for one variable. Let's solve the second equation for (y): (2x - y = 7) (y = 2x - 7)
Substitute this expression for (y) into the first equation: (3x + (2x - 7) = 8)
Solve for (x): (3x + 2x - 7 = 8) (5x - 7 = 8) (5x = 15) (x = 3)
Now, substitute the value of (x) into either equation to find (y). Let's use the first equation: (3(3) + y = 8) (9 + y = 8) (y = -1)
So, the solution to the system of equations is (x = 3) and (y = -1).
You can also represent the solution graphically by plotting the two equations on a graph and finding the point where they intersect.

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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.