the system of equations using the addition (elimination) method?

6x+2y=2
(-2)*[(3x+5y)]=(-2)*5

6x + 2y = 2 (A)
-6x - 10y =-10 (you add these two equations and you get):

(6x-6x)+(2y-10y)=2-10 ------>

0-8y=-8 -----> y=(-8)/(-8) -----> y=1

For y=1 if we replace in the equation (A) we get:

6x+(2*1)=2 -----> 6x+2=2 -----> 6x=2-2 ------>6x=0 ------> x=0

Thus the solution to the system of equations is the ordered pair:

(x,y)=(0,1)

x + 5y = 4 2x – 5y = 2 upload those 2 equations mutually 3x + 0 = 6 x = 2 replace x into 1st equation 2 + 5y = 4 y = 2/5 verify answer utilising 2d equation 2(2) – 5(2/5) = 2 4 – 2 = 2 2 = 2 (x, y) = (2, 2/5) QED

6x + 2y = 2
-2[3x + 5y = 5]

6x+2y=2
-6x-10y=-10

-8y=-8
y=1

6x+2=2
6x=0
x=0

(0,1)

6x + 2y = 2
- 6x - 10y = - 10-------ADD

- 8y = - 8
y = 1

3x + 5 = 5
x = 0

x = 0 , y = 1

Multiply the 2nd equation by -2 to get: -6x - 10y = -10. Now add this to the first equation:

6x + 2y = 2
-6x - 10y = -10
-------------------------
-8y = -8
y = 1

Substitute this into one of the equations (either will give the same answer) to obtain x:

6x + 2y = 2
6x + 2(1) = 2
6x + 2 = 2
6x = 0
x = 0.

(0, 1)

x=0
y=1

6x + 2y = 2
3x + 5y = 5

==> 3 (6x + 2y = 2)
==> 6 (3x + 5y = 5)

18x + 6y = 6
18x + 30y = 30
---minus-------

-24y = -24

y = 1

6x + 2(1) = 2

6x + 2 = 2

6x = 0

x = 0/6

x = 0

Solution set {0, 1} ANSWER.

6x + 2y = 2
3x + 5y = 5

3x + 5y = 5
-2(3x + 5y) = -2(5)
-6x - 10y = -10

...6x + 2y = 2
+) -6x - 10y = -10 (addition)
------------------------------
-8y = -8

-8y = -8
y = -8/-8
y = 1

3x + 5y = 5
3x + 5(1) = 5
3x + 5 = 5
3x = 5 - 5
x = 0/3
x = 0

∴ x = 0 , y = 1

6x + 2y = 2
-2 / 3x + 5y = 5 ---> multiply the equation by -2
___________________
6x + 2y = 2
-6x + (-10)y = -10
+__________________ ---> add the like terms
(-10+2)y =-10 +2 ---> x's are gone
-8y = -8
y = 1

--->substitute y in one of the equations
6x + 2y = 2
6x + (2*1) = 2
6x + 2 = 2
6x = 0
x = 0

---> so your ordered pair is (0,1) :)))