How do you solve the following linear system: # 1/2x+1/3y=13, 1/5x+1/8=5 #?

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Answer 1 · 2018-05-28T15:09:12

#x=10#
#y=24#

The easiest way to deal with these is to get rid of the fractions first:

I assume you forgot to py the y in the second equation.
#1/2x+1/3y=13, 1/5x+1/8y=5#

Multiply each equation by its common denominator:

#6(1/2x+1/3y=13)#

#3x + 2y =78#

#40(1/5x+1/8y=5)#

#8x + 5y = 200#

now that you have equations with integers use elimination:

#3x + 2y =78#
#8x + 5y = 200#

#-5(3x + 2y =78)#
#2(8x + 5y = 200)#

#-15x -10y = -390#
#16x+10y=400

#x=10#

#3x + 2y =78#
#3(10) + 2y =78#
#30 + 2y =78#
#2y =48#

#y=24#