How do you solve #2x+2y=14# and #2x-y=5# using substitution?

Question

Savannah Anderson · Accepted Answer

#x = 4, y = 3#

First you want to find a definition for either #x# or #y# in terms of the other, using the second equation.

#2x - y = 5# #2x = y + 5# #y = 2x - 5#

Now you can substitute this into the first equation.

#2x + 2y = 14# #2x + 2(2x - 5) = 14# #6x - 10 = 14# #6x = 24# #x = 4#

With this value, substitute into anything and it should give you #y#. Lets use the direct equation for #y# we found.

#y = 2x - 5# #y = 2 * 4 - 5# #y = 3#

You can substitute these values into any of the equations and they should work, if they are correct.

Jameson Allen · Answer

undefined To solve the system of equations 2x + 2y = 14 and 2x - y = 5 using substitution:

1. Solve one of the equations for one variable in terms of the other variable.
2. Substitute the expression found in step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Once you have found the value of one variable, substitute it back into one of the original equations to find the value of the other variable.
5. Verify the solution by substituting both values into both original equations to ensure they satisfy both equations.