Two methods are immediately obvious with the given equations.
1. Elimination
Note that the #x# terms are additive inverses.
Write each equation in the same form and add them.
#" "+x-4y = -15" "A#
#" "ul(-x-2y= + 3)" "B#
#A+B:color(white)(x)-6y = -12" "larr div -6#
#color(white)(xxx.xxxxx)y = 2#
Substitute the value for #y# into #x = 4y+15#
#x = 4(2)-15#
#x =-7#
2. Equating
Write each equation with #x# as the subject.
#color(blue)(x = 4y-15)" and "color(red)(x = -2y-3)#
#color(white)(xxxxxxxxx)color(blue)(x)=color(red)(x)#
#color(white)(xxxx)color(blue)(4y-15)" "=" "color(red)(-2y-3)#
#color(white)(xxxx)4y+2y=-3+15" "larr# equate the expressions for #x#x
#color(white)(xxxxxxx)6y = 12#
#color(white)(xxxxxxxx)y = 2#
#x= -2y-3#
#x = -2(2)-3#
#x = -7#
