How do you solve the system of equations #y= - 2x + 5# and #2y + 4x = 10#?

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Answer 1 · 2018-07-15T12:08:34

See a solution process below:

Step 1) Because the first equation is already solve for #y# we can substitute #(-2x + 5)# for #y# in second equation and solve for #x#:

#2y + 4x = 10# becomes:

#2(-2x + 5) + 4x = 10#

#(2 xx -2x) + (2 xx 5) + 4x = 10#

#-4x + 10 + 4x = 10#

#-4x + 10 - color(red)(10) + 4x = 10 - color(red)(10)#

#-4x + 0 + 4x = 0#

#-4x + 4x = 0#

#0 = 0#

Because this statement is true, #0# does equal #0#, this shows both equations are in fact different equations for the same line.

Therefore, there are an infinite number of solutions.