Solve the system of equations:
#y=-4x+9# and #-x-12y=-14#
The first equation gives a value for #y# that can be substituted into the second equation.
#-x-12y=-14#
Multiply both sides by #-1#. This will change each sign to its opposite.
#x+12y=14#
Substitute #-4x+9# for #y# in the second equation.
#x+12(-4x+9)=14#
Expand.
#x-48x+108=14#
Subtract #108# from both sides.
#x-48x+color(red)cancel(color(black)(108))-color(red)cancel(color(black)(108))=14-108#
Simplify.
#-47x=-94#
Divide both sides by #-47#.
#color(red)cancel(color(black)((-47)color(black)(x)))/color(red)cancel(color(black)(-47))=(-94)/(-47)# #lArr# A negative divided by another negative produces a positive result.
Simplify.
#color(red)(x)=-94/-47#
#color(red)(x)=color(red)2#
Now substitute #2# for #x# into the first equation to solve for #y#.
#color(purple)(y)=-4*color(red)2+9#
#color(purple)(y)=-8+9#
#color(purple)y=color(purple)(1#
Check the answer with both equations.
First equation.
#color(purple)(y)=-4color(red)x+9#
#1=-4*color(red)2+9#
Simplify.
#1=-8+9#
#1=1# Check
Second equation.
#color(red)(-x)-12color(purple)y=-14#
#-color(red)2-12*color(purple)1=-14#
#-2-12=-14#
#-14=-14# Check
