How do you solve the system of equations #13x + 9y = 155# and #14x + 10y = 166#?

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Answer 1 · 2017-06-21T19:04:53

#(986,-1407)#

The first step is to solve one of the equations (it doesn't matter which one) for #y# in terms of #x#.

#14x+10y=166#

Subtract #10y# from both sides

#14x= -10y+166#

Divide both sides by 14

#x=-10/14y-166/14#

Reduce the fractions to lowest terms

#x=-5/7y-133/7#

Next, take the expression equal to #x# and plug it into the other equation.

#13color(red)(x)+9y=155#

#13(color(red)(-5/7y-133/7))+9y=155#

#-65/7y-1729/7+9y=155#

Multiply everything by #7# to get rid of all fractions

#-65y-1729+63y=1085#

Combine like terms

#-2y=2814#

Divide both sides by #-2#

#y=-1407#

Finally, plug this value for #y# back into the equation for #x#

#x=-5/7color(red)(y)-133/7#

#x=-5/7(color(red)(-1407))-19#

#x=-5(-201)-19#

#x=1005-19#

#x=986#

So the solution to both equations is #(986,-1407)#