which method would be the simplest way to solve the system?
7x + 5y =19
-7x- 2y = -16
The simplest way to solve the system of equations is by using the method of elimination, in which you add or subtract the equations to eliminate one of the variables. In this case, by adding both equations, you can directly eliminate the x variable because the coefficients of x in both equations are opposites of each other.
Here are the equations:
7x + 5y = 19
-7x - 2y = -16
Now add the two equations together:
(7x + 5y) + (-7x - 2y) = 19 + (-16)
7x - 7x + 5y - 2y = 3
0x + 3y = 3
Now you're left with a single variable equation:
3y = 3
To solve for y, divide both sides by the coefficient of y, which is 3:
3y / 3 = 3 / 3
y = 1
Now that we have the value of y, substitute it back into one of the original equations to find the value of x. We can use the first equation:
7x + 5(1) = 19
7x + 5 = 19
7x = 19 - 5
7x = 14
Divide by 7 to get the value of x:
7x / 7 = 14 / 7
x = 2
Thus, the solution to the system of equations is x = 2 and y = 1.