How do you solve the system #x-2y=3# and #4x-8y=12# using substitution?

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Answer 1 · 2018-06-03T22:28:01

See a solution process below:

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

#x - 2y = 3#

#x - 2y + color(red)(2y) = 3 + color(red)(2y)#

#x - 0 = 3 + 2y#

#x = 3 + 2y#

Step 2) Substitute #(3 + 2y)# for #x# in the second equation and solve for #y#:

#4x - 8y = 12# becomes:

#4(3 + 2y) - 8y = 12#

#(4 * 3) + (4 * 2y) - 8y = 12#

#12 + 8y - 8y = 12#

#12 + 0 = 12#

#12 = 12#

This indicates there is an infinite number of solutions because these lines are in fact the same line.