Question

Solve the following systems of equations using the addition (elimination) method.
What type of system is it? Name the solution if there is one.
2x-5y=15
x-7y=3

Answer 1

multiply the second equation by negative 2 to get -2x + 14y = -6. Then add (technically subtract) the two equations

Answer 2

the goal is to eliminate a variable by adding the 2 equations together
you can force the coefficients to add to zero by multiplying equations by some scalar number

If you want to get rid of the "x", you need 2x + (-2x) = 0 , right now its 2x +x = 3x
this means you must multiply 2nd equation by "-2"

---> 2x -5y =15
-2x +14y = -6
---------------------
0 +9y = 9

Now you have single variable equation where you can easily solve for "y"
---> y = 1

Substitute back in to solve for "x"
--> 2x -5(1) = 15
---> x = 10

system has 1 solution (10,1) so it is an independent consistent system