How do solve the following linear system?: # 4x+3y=1 , 2x +5y - 21 = 0 #?

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Answer 1 · 2016-04-15T07:43:48

#x=(-116)/28#
#y=41/7#

Given -

#4x+3y=1# ---------- (1)
#2x+5y-21=0# -------- (2)

Take the constant term to the left in equation (1)

#4x+3y-1=0#

Let us use elimination method to solve the equations.

Multiply equation (2) with 2

#2x+5y-21=0# -------- (2) #xx 2#
#4x+10y-42=0#

Equate both the equations

#4x+3y-1=4x+10y-42#

Take constant terms to right and other terms to left.

#4x+3y-4x-10y=-42+1#

Simplify -

#-7y=-41#
#y=(-41)/(-7)=41/7#
#y=41/7#

Substitute #y=41/7# in equation (1)

#4x+3(41/7)=1#
#4x+123/7=1#
#4x=1-123/7=(-116)/7#

#x=(-116)/7 xx 1/4 = (-116)/28#
#x=(-116)/28#