How do solve the following linear system?: # -10x+7y=-2 , -4x-15y=-1 #?

1 Answer
Mar 5, 2016

Answer:

#x = 37/178#
#y = 1/89#

Explanation:

Scale either equation (or both) with the goal of eliminating one of the variables

#[1] -10x + 7y = -2#

#[2] -4x - 15y = -1#

Multiply #[1]# by -2 and multiply #[2]# by 5

#[1'] -2(-10x + 7y = -2)#

#=> [1'] 20x -14y = 4#

#[2'] 5(-4x - 15y = -1)#

#=> [2'] -20x - 75y = -5#


#[1'] 20x -14y = 4#
#[2'] -20x - 75y = -5#

If we add both equations, #x# will be eliminated and we can solve for y

#[3] -89y = -1#

#=> y = 1/89#

To get #x#, substitute the obtained value for #y# in one of the equations #[1]#, #[1']#, #[2]#, #[2']#. For example, let's use #[1]#

#-10x + 7y = -2#

#=> -10x + 7(1/89) = -2#

#=:> -10x + 7/89 = -2#

#=> 10x = 2 + 7/89#

#=> 10x = (178 + 7)/89#

#=> 10x = 185/89#

#=> x = 37/178#