How do you solve the following system: #-6x-2y=-14, 4x-5y= -1 #?

To solve the system of equations:

1. Choose one of the equations and solve it for one variable in terms of the other.
2. Substitute the expression obtained in step 1 into the other equation.
3. Solve the resulting equation for the variable.
4. Once you have the value of one variable, substitute it back into either of the original equations to find the value of the other variable.
5. Write the solution as an ordered pair (x, y).

Solution:

1. From the first equation, solve for x: (-6x - 2y = -14) (x = \frac{-14 + 2y}{-6})

2. Substitute (x) from step 1 into the second equation: (4\left(\frac{-14 + 2y}{-6}\right) - 5y = -1)

3. Solve for (y): (4\left(\frac{-14 + 2y}{-6}\right) - 5y = -1) (4(-14 + 2y) + 30y = -6) (-56 + 8y + 30y = -6) (38y = 50) (y = \frac{50}{38})

4. Substitute (y) back into the expression for (x): (x = \frac{-14 + 2 \cdot \frac{50}{38}}{-6}) (x = \frac{-14 + \frac{100}{38}}{-6}) (x = \frac{-14 + \frac{50}{19}}{-6}) (x = \frac{-266}{114})

5. The solution is (\left(\frac{-266}{114}, \frac{50}{38}\right)), which can be simplified to (\left(\frac{-133}{57}, \frac{25}{19}\right)).