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

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Answer 1 · 2018-06-12T10:46:54

#x= 1, y = 2#

#5x - y = 3, # Eqn (1)

#x + 2y = 5# Eqn (2)

# 10x - 2y = 6# Eqn (1) * 2= Eqn (3)

Add Eqns (2) & (3),

#x + 10x + cancel(2y) - cancel(2y) = 5 + 6#

#11x = 11# or #x = 1#

Substituting value of x in Eqn (1),

#5 - y = 3#

#y = 2#

Answer 2 · 2018-06-12T11:19:24

Let's solve for #y#

#1^(st) " equation "#

#5x-y=3#

#-y=3-5x#

Multiply both sides by #-1#

#color(magenta)(y=5x-3#

Now to the second equation

#x+2y=5#

Put #y's# value

#x + (2xx(5x-3))=5#

Notice that the brackets change everything

Solve

#x+10x-6=5#

#11x-6=5#

#11x=11#

#color(red)(x=1#

Now....

#y=5x-3#

Put #x's# value

#y = 5xx1-3#

#y=5-3#

#color(red)(y=2#