Question 31879
Ohhh ... I love this one ...
if angles are complementary ... when added they equal 90 deg.
and if you have two sets of them ... the equal 180 degrees
1. L+M=90
2. N+P=90
3. L+M+N+P=180
4. L=y-2
5. M=2x+3
6. N=2x-y
7. P=x-1
Plug equations 4, 5, 6, and 7 into equation 3 
{{{ L+M+N+P=180 }}}
{{{ 1y - 2 + 2x + 3 + 2x - 1y + 1x - 1 = 180 }}}
To better combine like terms ... rearange the numbers
{{{ 2x + 2x + 1x + 1y - 1y - 2 + 3 - 1 = 180 }}}
combine like terms (y's and constants cancel out)
{{{ 5x = 180 }}}
Divide by 5
{{{ x = 36 }}}
Plug this back into equations 5 and 7
{{{ M=2x+3 }}} and {{{ P=x-1 }}}
{{{ M=2(36)+3 }}} and {{{ P=36-1 }}}
{{{ M=72+3 }}} and {{{ P=35 }}}
{{{ M=75 }}}
Take the M and P values and plug them back into equations 1 and 2
{{{ L+M=90 }}} and {{{ N+P=90 }}}
{{{ L+75=90 }}} and {{{ N+35=90 }}}
{{{ L=15 }}} and {{{ N=55 }}}
Plug these values back into equations 4 and 6 and solve (don't forget the x)
{{{ L=y-2 }}} and {{{ N=2x-y }}}
{{{ 15=y-2 }}} and {{{ 55=2(36)-y }}}
{{{ 17=y }}} and {{{ 55=72-y }}}
{{{ 17=y }}} and {{{ -17=-y }}}
{{{ 17=y }}} and {{{ 17=y }}}
OKAY ..... Looking back through ...
x=36
y=17
L=15
M=75
N=55
P=35