1. Solve one equation for one of the variables.

2. Substitute that value for the variable in the second equation.

3. Solve the second equation for the remaining variable.

4. Substitute that value into the first equation to find the value of the first variable.

1. 6x - 5y = 3

6x = 5y + 3

x = (5/6)y + 1/2

2. 4x + 3y = 21 (sub (5/6)y + 1/2 for x)

4((5/6)y + 1/2) + 3y = 21

(20/6)y + 2 + 3y = 21

(10/3) y + (9/3)y = 19

19y = 57

y = 3

x = (5/6)y + 1/2

x = (5/6)* 3 + 1/2 = 5/2 + 1/2 = 6/2 = 3