How do solve the following linear system?: # -4x-2y=14 , -10x+7y=-2 #?

1 Answer
Jan 24, 2018

Answer:

See a solution process below:

Explanation:

Step 1) Solve the first equation for #y#:

#-4x - 2y = 14#

#color(red)(-1/2)(-4x - 2y) = color(red)(-1/2) xx 14#

#(color(red)(-1/2) xx -4x) + (color(red)(-1/2) xx -2y) = -7#

#2x + 1y = -7#

#2x + y = -7#

#2x - color(red)(2x) + y = -7 - color(red)(2x)#

#0 + y = -7 - 2x#

#y = -7 - 2x#

Step 2) Substitute #(-7 - 2x)# for #y# in the second equation and solve for #x#:

#-10x + 7y = -2# becomes:

#-10x + 7(-7 - 2x) = -2#

#-10x + (7 xx -7) + (7 xx -2x) = -2#

#-10x + (-49) + (-14x) = -2#

#-10x - 49 - 14x = -2#

#-10x - 14x - 49 = -2#

#(-10 - 14)x - 49 = -2#

#-24x - 49 = -2#

#-24x - 49 + color(red)(49) = -2 + color(red)(49)#

#-24x - 0 = 47#

#-24x = 47#

#(-24x)/color(red)(-24) = 47/color(red)(-24)#

#(color(red)(cancel(color(black)(-24)))x)/cancel(color(red)(-24)) = -47/24#

#x = -47/24#

Step 3) Substitute #-47/24# for #x# in the solution to the first equation at the end of Step 1:

#y = -7 - 2x# becomes:

#y = -7 - (2 xx -47/24)#

#y = -7 - (-47/12)#

#y = -7 + 47/12#

#y = (12/12 xx -7) + 47/12#

#y = -84/12 + 47/12#

#y = -37/12#

The Solution Is:

#x = -47/24# and #y = -37/12#

Or

#(-47/24, -37/12)#