How do you solve the system of equations #4x - 5y = 25# and # - 7x + 3y = 8#?

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Answer 1 · 2018-02-13T14:28:07

#x=-5 and y =-9#

#4x - 5y = 25#------------(1)

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

First eliminate any one variable (say #y#),

#(1) xx 3 + (2) xx 5 =>#

#=>12x - 15y -35x + 15y =75 + 40#

#=> 12x-35x -cancel(15y)+cancel(15y) = 115#

#=> -23 x =115#

#=> x = -5#

Substitute this value of #x# in any one equation.

(1) #=> 4xx(-5) -5y =25#

#=> -20 -5y =25#

#=> y = (25+20)/-5#

#y = -9#

So, #x=-5 and y =-9#

Verify by substituting both values in equation (2):

Left hand side of equation = #-7x+3y#

#=> -7xx(-5) +3xx(-9) = 35 - 27 = 8 #= Right hand side.

Hence verified.