what is the solution of the system?
7x + 5y = 19
-7x - 2y = -16
a ) (2,1)
b ) (1,2)
c ) (7,5)
d ) (-7,-2)
To find the solution of the system of equations, we can directly add both equations since the terms with 'x' will cancel each other out, and we will be left with an equation in just 'y'.
Adding the two equations:
7x + 5y = 19
-7x - 2y = -16
-------------
0 + 3y = 3
Now solve for 'y':
3y = 3
y = 1
Now that we have the value for 'y', we can substitute it back into either of the original equations to find 'x'. We'll use the first equation:
7x + 5y = 19
7x + 5(1) = 19
7x + 5 = 19
7x = 19 - 5
7x = 14
x = 14 / 7
x = 2
So, the solution of the system is (x, y) = (2, 1), which corresponds to option:
a ) (2,1)