What is the value of the x variable in the solution to the following system of equations?
2x + 2y = 6
x + 3y = −1

−2
2
5
−5
11. [6.03] Solve the following system.
x − y = 10
x + y = 8

(−9, 1)
(9, −1)
(9, 1)
(−1, 9)

Question

What is the value of the x variable in the solution to the following system of equations?
2x + 2y = 6
  x + 3y = −1
 	
	−2
	2
	5
	−5
11. 	[6.03] Solve the following system.
x − y = 10
x + y = 8
 	
	(−9, 1)
	(9, −1)
	(9, 1)
	(−1, 9)

michele_laino · Answer

question #1
here  I solve the second equation for x, and I get:
x=-1-3y
then I substitutte into the first equation, and I get:
$$2\left( { - 1 - 3y} \right) + 2y = 6$$
what is y?

triciaal · Answer

2x + 2y = 6
  x + 3y = −1
can simplify the first eqn by dividing by 2 so x + y = 3 
subtract from the 2nd eqn   2y = -4 so y = -2
substitute in either original  x = -1 -3(-2) = 5
check solution

triciaal · Answer

x − y = 10
x + y = 8
coefficient of y already equal and opposite so just add eqns to eliminate y 
2x = 18 so x = 9 
substitute for x in either 
y = -1