How do you solve the following linear system: # 8x - 7y = -3 , 6x - 5y = -1 #?

1 Answer
radee
Mar 7, 2016

#(4, 5)#

Explanation:

In order to solve systems of linear equations, we can use either of the three methods (1) elimination, (2) substitution, and (3) graphing. For this question I would use the elimination because I am more used to it and I think that it is quicker to do but note that using any of the three methods would give you the same result.

[Solution]
#8x - 7y = -3#
#6x - 5y = -1#

Multiplying the first equation by 3 and multiplying the second equation by 4 would make the coefficients of the first terms of both equations 24. This would allow us to eliminate the #x# variable so we can solve for the #y#.

#24x - 21y = -9#
#24x - 20y = -4#

Subtracting the two equations...

#-y = -5#
#y = 5#

Once we get the value of #y# we would then substitute it to any of the two equations to solve for #x#. In this case, I would use the second equation since it has a smaller coefficient hence would produce smaller values.

#6x - 5y = -1#
#6x - 5(5) = -1#
#6x - 25 = -1#
#6x = -1 + 25#
#6x = 24#
#x = 4#

#(4, 5)#

[Checking byt substituting #(4,5)#]
#8x - 7y = -3#
#6x - 5y = -1#

*First Equation
#8(4) - 7(5) = -3#
#32 - 35 = -3#
#-3 = -3#

*Second Equation
#6x - 5y = -1#
#6(4) - 5(5) = -1#
#24 - 25 = -1#
#-1 = -1#

Since both equations were satisfied by the computed values, we know that our answer is correct!

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