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

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Answer 1 · 2016-08-03T22:33:09

$x = - 43, y = - 6$ $x= -43, y = -6$

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

Make #2x" the subject of each equation:

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

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

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

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

Solve for y:

$- y + 2 y = - 98 + 92$ $-y +2y = -98+92$

$y = - 6$ $" "y = -6$

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

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

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

$x = - 43$ $x = -43$

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