Solve the system using elimination.
6x-2y = 28
5x + 7y = 6
The solution is (Simplify your answer. Type an ordered pair.)
To solve the system using elimination, we need to eliminate one variable by adding or subtracting the equations.
Multiply the first equation by 5:
5(6x-2y) = 5(28)
30x - 10y = 140
Now, multiply the second equation by 6:
6(5x + 7y) = 6(6)
30x + 42y = 36
By subtracting the second equation from the first, the x variable will be eliminated:
(30x - 10y) - (30x + 42y) = 140 - 36
30x - 10y - 30x - 42y = 104
-52y = 104
y = 104 / -52
y = -2
Now we can substitute the value of y back into one of the original equations:
6x - 2(-2) = 28
6x + 4 = 28
6x = 28 - 4
6x = 24
x = 24 / 6
x = 4
Therefore, the solution to the system of equations is (4, -2).