How do you find the solution of the system of equations #y = x+1# and #y = 2x -1#?

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Answer 1 · 2017-03-04T01:38:18

See the entire solution process below:

Step 1) Because the first equation is already solve for #y#, substitute #x + 1# for #y# in the second equation and solve for #x#:

#y = 2x - 1# becomes:

#x + 1 = 2x - 1#

#x + 1 - color(red)(x) + color(blue)(1) = 2x - 1 - color(red)(x) + color(blue)(1)#

#x - color(red)(x) + 1 + color(blue)(1) = 2x - color(red)(x) - 1 + color(blue)(1)#

#0 + 2 = x - 0#

#2 = x#

#x = 2#

Step 2) Substitute #2# for #x# in the first equation and calculate #y#:

#y = x + 1# becomes:

#y = 2 + 1#

#y = 3#

The solution is: #x = 2# and #y = 3# or #(2, 3)#