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

Question

Savannah Anderson · Accepted Answer

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)#

Eva Adamson · Answer

undefined To find the solution of the system of equations y = x+1 and y = 2x -1, you can set the equations equal to each other:

x + 1 = 2x - 1

Then, solve for x:

x = 2

Once you have the value of x, you can substitute it into one of the original equations to find the value of y:

y = 2(2) - 1 
y = 4 - 1 
y = 3

So, the solution to the system of equations is x = 2 and y = 3.