Another method of solving a system of equations is by elimination.
Eliminating one of the variables is achieved by adding or subtracting two equations to form a third one.
Try to create ADDITIVE INVERSES first!
Additive inverses add to give 0.
#-3x +3x = 0" or " (+8y) +(-8y) =0#
#color(white)(xxxxxxx.)3xcolor(red)(+4y) = -7# ..........................A
#color(white)(xxxxxxxx)xcolor(red)(-2y) = +1# ............................B (re-arranged)
#color(white)(xxxxxxxxxx)uarr#
Multiplying B by 2 will give us additive inverses.
#Bxx2:rarrcolor(white)(x.)2xcolor(red)(-4y)=+2#...........................C
#color(white)(xxxxxxxx.)3xcolor(redx)(+4y) = -7# ..........................A
Now add them:
#A+C:rarrcolor(white)(x)5x" "= -5" "larr# solve for x
#A+C:rarrcolor(white)(xx)x" "= -1" "larr# one variable solved!
Now substitute this value for #x# into any equation to find #y#
#3x+4y = -7" "rarr 3(-1) +4y = -7#
#color(white)(xxxxxxxxxxxxxxx)-3+4y = -7#
#color(white)(xxxxxxxxxxxxxxxxxxxx)4y = -7+3#
#color(white)(xxxxxxxxxxxxxxxxxxxx)4y = -4#
#color(white)(xxxxxxxxxxxxxxxxxxxxx)y = -1" "larr# variable solved
#x=-1 and y=-1#
