solve using the elimination method. show your work. if the system has no solution or an infinite number of solutions, state this x+y=10

x-y=2

x+y = 10

x-y = 2 add
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2 x + 0 y = 12

x = 6
y = 4

3r+5s=

To solve the system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations.

Given equations:
1) x + y = 10
2) x - y = 2

To eliminate the variable 'y', we can add the two equations together.

Add equation 1 and equation 2:
(x + y) + (x - y) = 10 + 2
x + y + x - y = 12
2x = 12

Divide both sides by 2 to solve for 'x':
2x/2 = 12/2
x = 6

Now that we have the value of 'x', we can substitute it back into any of the original equations to find the value of 'y'.

Let's use equation 1:
x + y = 10
6 + y = 10

Subtract 6 from both sides to solve for 'y':
y = 10 - 6
y = 4

Therefore, the solution to the system of equations is x = 6 and y = 4.

There are no infinite solutions or no solution in this case.