Elimination Method : In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
The given system of equations :
5x + y = 9 ( 1 )
5x - y = 1 ( 2 )
Add equation (1) & (2)
5x + y + (5x - y) = 9 + 1
5x + y + 5x - y = 10
10x +y - y = 10
10x + 0 = 10
x = 10/10
x = 1
Substitute the value of x = 1 in the equation (1)
5x + y = 9
5(1) + y = 9
5 + y = 9
y = 9 - 5
y = 4
Answer : (x, y) = (1, 4)