Question

Solve the system using elimination.
6x-2y = 28
5x + 7y = 6
The solution is (Simplify your answer. Type an ordered pair.)

Answer 1

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).