How do you solve the following system: #7y − 6x − 5 = 0, y + 4x = 16 #?

1 Answer
May 21, 2017

Answer:

See a solution process below:

Explanation:

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

#y + 4x = 16#

#y + 4x - color(red)(4x) = 16 - color(red)(4x)#

#y + 0 = 16 - 4x#

#y = 16 - 4x#

Step 2) Substitute #(16 - 4x)# for #y# in the first equation and solve for #x#:

#7y - 6x - 5 = 0# becomes:

#7(16 - 4x) - 6x - 5 = 0#

#(7 * 16) - (7 * 4x) - 6x - 5 = 0#

#112 - 28x - 6x - 5 = 0#

#112 - 5 - 28x - 6x = 0#

#(112 - 5) + (-28 - 6)x = 0#

#107 + (-34)x = 0#

#107 + (-34)x + color(red)(34x) = 0 + color(red)(34x)#

#107 + 0 = 34x#

#107 = 34x#

#107/color(red)(34) = (34x)/color(red)(34)#

#107/34 = (color(red)(cancel(color(black)(34)))x)/cancel(color(red)(34))#

#107/34 = x#

#x = 107/34#

Step 3) Substitute #107/34# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:

#y = 16 - 4x# becomes:

#y = 16 - (4 xx 107/34)#

#y = (34/34 xx 16) - 428/34#

#y = 544/34 - 428/34#

#y = 116/34#

#y = (2 xx 58)/(2 xx 17)#

#y = (color(red)(cancel(color(black)(2))) xx 58)/(color(red)(cancel(color(black)(2))) xx 17)#

#y = 58/17#

The solution is: #x = 107/34# and #y = 58/17# or #(107/34, 58/17)#