How do you solve #2x+y= -92# and #2x+2y= -98# using substitution?

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Answer 1 · 2016-08-03T22:33:09

#x= -43, y = -6#

It is useful to notice that both the given equations have a #2x# term.

Make #2x" the subject of each equation:

#color(blue)(2x = -y-92)" and "color(red)(2x = -2y-98)#

Obviously #color(blue)(2x) = color(red)(2x) # but we can use this to form a new equation.

#" if " color(blue)(2x) " " = " "color(red)(2x)#

Then: #" " color(blue)(-y -92) = color(red)(-2y-98)#

Solve for y:

# -y +2y = -98+92#

#" "y = -6#

Now use #y=-6# to solve for #x#

#color(blue)(2x = -(-6)-92)#

#color(blue)(2x = 6-92) =-86

#x = -43#