How do you solve 2x + 3y = 2 and x + 6y = 4?

1 Answer
Jun 16, 2018

Answer:

See a solution process below:

Explanation:

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

#x + 6y = 4#

#x + 6y - color(red)(6y) = 4 - color(red)(6y)#

#x + 0 = 4 - 6y#

#x = 4 - 6y#

Step 2) Substitute #(4 - 6y)# for #x# in the first equation and solve for #y#:

#2x + 3y = 2# becomes:

#2(4 - 6y) + 3y = 2#

#(2 xx 4) - (2 xx 6y) + 3y = 2#

#8 - 12y + 3y = 2#

#8 + (-12 + 3)y = 2#

#8 + (-9)y = 2#

#8 - 9y = 2#

#8 - color(red)(8) - 9y = 2 - color(red)(8)#

#0 - 9y = -6#

#-9y = -6#

#(-9y)/color(red)(-9) = (-6)/color(red)(-9)#

#y = 2/3#

Step 3) Substitute #2/3# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#:

#x = 4 - 6y# becomes:

#x = 4 - (6 xx 2/3)#

#x = 4 - 12/3#

#x = 4 - 4#

#x = 0#

The Solution Is:

#x = 0# and #y = 2/3#

Or

#(0, 2/3)#