im stuck on this

Question

Solve the following system by the addition method. (If there is no unique solution, enter DEPENDENT. If the system is inconsistent, enter NO SOLUTION.)

 

7x +y = 8
2x - y = 1


(x, y) = 

Answer 1

Hello Corina,

 

7x +y = 8
2x - y = 1

 

The addition method, aka the elimination method is one where you add the two equations together, eliminating one of the variables.  In this case we have a +y in one equation and a -y in the other, so adding the two equations together will eliminate the y variable.

 

7x +y = 8
2x - y = 1

------------

9x = 9

 

Divide by 9 and

x = 1

 

Now substitute this value of x in one of the original equations and solve for y.

7x + y = 8

7(1) + y = 8

7+y=8

y = 1

 

The solution is (1,1).