Question

What does the equation become when one variable is eliminated from the system of equations below?

6x + 3y = 7
5x - 3y = 3
A. 11x = 10
B. 3x = 10
C. 4x = 10
D. 3y = 3

Answer 1

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.