How do you solve the system of equations #y= 8x + 11# and #y = - 5x - 15#?

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Answer 1 · 2017-01-30T06:06:58

See the entire solution process below:

Step 1) Because the first equation is already solved for #y#, substitute #(8x + 11)# for #y# in the second equation and solve for #x#:

#8x + 11 = -5x - 15#

#8x + 11 - color(blue)(11) + color(red)(5x) = -5x - 15 - color(blue)(11) + color(red)(5x)#

#8x + color(red)(5x) + 11 - color(blue)(11) = -5x + color(red)(5x) - 15 - color(blue)(11)#

#13x + 0 = 0 - 26#

#13x = -26#

#(13x)/color(red)(13) = -26/color(red)(13)#

#(color(red)(cancel(color(black)(13)))x)/cancel(color(red)(13)) = -2#

#x = -2#

Step 2) Substitute #-2# for #x# in the first equation and calculate #y#:

#y = (8 xx -2) + 11#

#y = -16 + 11#

#y = -5#

The solution is:

#x = -2# and #y = -5#