How do you solve by substitution #5x-6y=6# and #5x+y=2#?

#5x-6y=6# --- (1)
#5x+y=2# --- (2)

(1) minus (2)

#-6y-y=6-2#
#-7y=4#
#y=-4/7# --- (3)

Sub (3) into (1)

#5x-6times-4/7=6#
#5x+24/7=6#
#5x=18/7#
#x=18/35#

Solve the system of equations.

#"Equation 1":# #5x-6y=6#

#"Equation 2":# #5x+y=2#

The solution to the system of linear equations is the point they have in common, the point of intersection. The system will be solved using substitution.

Solve Equation 2 for #y#.

#y=-5x+2#

Substitute #-5x+2# for #y# in Equation 1. Solve for #x#.

#5x-6(-5x+2)=6#

Expand.

#5x+30x-12=6#

Simplify.

#35x-12=6#

Add #12# to both sides.

#35x=6+12#

Simplify.

#35x=18#

Divide both sides by #35#.

#x=18/35# or #0.514#

Substitute #18/35# for #x# in Equation 2. Solve for #y#.

#5(18/35)+y=2#

Simplify #color(red)cancel(color(black)(5))^1(18/color(red)cancel(color(black)(35))^7)# to #18/7#.

#18/7+y=2#

Multiply both sides by #7#.

#color(red)cancel(color(black)(7))^1xx18/color(red)cancel(color(black)(7))^1+7xxy=2xx7#

Simplify.

#18+7y=14#

Subtract #18# from both sides.

#7y=14-18#

Simplify.

#7y=-4#

Divide both sides by #7#.

#y=-4/7# or #-0.571#

Solution

#(18/35,-4/7)# or #(0.514,-0.571)#

graph{(y-5/6x+1)(y+5x-2)=0 [-10, 10, -5, 5]}