How do you solve the following linear system: # x+8y=3, 4x+5y=-2 #?

1 Answer
Apr 30, 2017

Answer:

See the solution process below:

Explanation:

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

#x + 8y = 3#

#x + 8y - color(red)(8y) = 3 - color(red)(8y)#

#x + 0 = 3 - 8y#

#x = 3 - 8y#

Step 2) Subsitute #3 - 8y# for #x# in the second equation and solve for #y#:

#4x + 5y = -2# becomes:

#4(3 - 8y) + 5y = -2#

#(4 * 3) - (4 * 8y) + 5y = -2#

#12 - 32y + 5y = -2#

#12 + (-32 + 5)y = -2#

#12 - 27y = -2#

#-color(red)(12) + 12 - 27y = -color(red)(12) - 2#

#0 - 27y = -14#

#-27y = -14#

#(-27y)/color(red)(-27) = (-14)/color(red)(-27)#

#(color(red)(cancel(color(black)(-27)))y)/cancel(color(red)(-27)) = 14/27#

#y = 14/27#

Step 3) Substitute #14/27# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:

#x = 3 - 8y# becomes:

#x = 3 - (8 * 14/27)#

#x = 3 - 112/27#

#x = (3 * 27/27) - 112/27#

#x = 81/27 - 112/27#

#x = -31/27#

The solution is: #x = -31/27# and #y = 14/27# or #(-31/27, 14/27)#