What is the solution to the following system of linear equations: #4x-y=-6# #x-2y=-5#?
1 Answer
Explanation:
Your starting system of equations looks like this
#{(4x-y = -6), (x-2y = -5) :}#
Multiply the first equation by
#{(4x-y = -6 | * (-2)), (x-2y = -5) :}#
#{(-8x+2y = 12), (" "x-2y = -5) :}#
Notice that if you add the two equations by adding the left-hand sides and the right-hand sides separately, you can eliminate the
The resulting equation will have only one unknown,
#{(-8x+2y = 12), (" "x-2y = -5) :}#
#stackrel("-------------------------------------------")#
#-8x + color(red)(cancel(color(black)(2y))) + x - color(red)(cancel(color(black)(2y))) = 12 + (-5)#
#-7x = 7 implies x = 7/((-7)) = color(green)(-1)#
Plug this value of
#4 * (-1) - y = -6#
#-4 - y = -6#
#-y = -2 implies y = ((-2))/((-1)) = color(green)(2)#
The solution set for this system of equations will thus be
#{(x=-1), (y=2) :}#