How do you solve the system of equations #x + 8y = 26# and #2x + y = 5#?

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Answer 1 · 2018-08-05T03:51:25

The solution is #(14/15, 47/15)#.

Equation 1: #x+8y=26#

Equation 2: #2x+y=5#

I am going to use elimination and substitution to answer this question.

Multiply Equation 1 by #-2#.

#-2(x+8y)=26xx-2#

#-2x-16y=-52#

Add the equations.

#-2x-16y=-52#
#color(white)(..)##2x+color(white)(..)y=color(white)(......)5#
#-------#
#-15ycolor(white)(.........)=-47#

Divide both sides by #-15#.

#y=(-47)/(-15)#

#y=47/15#

Substitute #47/15# for #y# in Equation 1 and solve for #x#.

#x+8(47/15)=26#

#x+376/15=26#

Subtract #376/15# from both sides.

#x=-376/15+26#

Multiply #26# by #15/15#.

#x=-376/15+26xx15/15#

#x=-376/15+390/15#

#x=14/15#

Solution: #(14/15, 47/15)#

graph{(x+8y-26)(2x+y-5)=0 [-10, 10, -5, 5]}