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

$x = -43$

How do you solve 2x+y= -922x+y= -92 and 2x+2y= -982x+2y= -98 using substitution?