Final answer:
By adding the two given equations, the variable y is eliminated, resulting in the equation 11x = 10.
Step-by-step explanation:
To eliminate one variable from the system of equations, you can add or subtract the equations from each other. In this case:
6x + 3y = 7
5x - 3y = 3
By adding these two equations, 3y and -3y cancel each other out, and we get:
6x + 5x = 7 + 3
11x = 10
Therefore, the equation becomes 11x = 10 after one variable is eliminated. Consequently, the elimination process results in a single equation, 11x = 10, consolidating the relationship between x and y into a single variable, x. This method streamlines the system, offering a clearer pathway to solving for the remaining variable by reducing the equations to a more manageable form.