which method would be the simplest way to solve the system?
7x + 5y = 19
-7x - 2y = -16
One of the simplest and most efficient methods to solve this system is to eliminate one variable by adding the two equations together. In this case, by adding both equations, we can eliminate the x-variable:
(7x + 5y) + (-7x - 2y) = 19 + (-16)
(7x - 7x) + (5y - 2y) = 19 - 16
0x + 3y = 3
3y = 3
Therefore, y = 1.
Substituting this value of y into one of the original equations, we can find the value of x:
7x + 5(1) = 19
7x + 5 = 19
7x = 14
x = 2.
Thus, the solution to the system of equations is x = 2 and y = 1.