Let's solve the system of equations:

Step 1: Simplify the equations

1. The first equation is already in a simplified form: $4x + 2y = -6$

2. For the second equation, distribute $-4$ to simplify: $-6x + y = -4(x - 2)$ Expand: $-6x + y = -4x + 8$ Simplify: $-6x + y + 4x = 8$ $-2x + y = 8$

So, the system of equations becomes: $4x + 2y = -6$ $-2x + y = 8$

Step 2: Solve the system

Multiply the second equation to align coefficients of $y$:

Multiply the second equation by $2$ to eliminate $y$ when added to the first equation: $4x + 2y = -6$ $-4x + 2y = 16$

Add the two equations:

$(4x - 4x) + (2y + 2y) = -6 + 16$ $4y = 10$ $y = \frac{10}{4} = \frac{5}{2}$

Substitute $y = \frac{5}{2}$ into one of the original equations:

Use the second simplified equation: $-2x + y = 8$ Substitute $y = \frac{5}{2}$: $-2x + \frac{5}{2} = 8$ Simplify: $-2x = 8 - \frac{5}{2}$ $-2x = \frac{16}{2} - \frac{5}{2}$ $-2x = \frac{11}{2}$ Solve for $x$: $x = -\frac{11}{4}$

Final Solution:

$x = -\frac{11}{4}, \quad y = \frac{5}{2}$

Would you like a step-by-step explanation or a graph of this system?

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Related Questions:

1. How can you graphically verify the solution of a system of equations?
2. What are some methods to solve systems of linear equations apart from substitution and elimination?
3. How can you check if a system of equations has no solution or infinitely many solutions?
4. How does multiplying an equation affect its solutions in a system?
5. What are practical applications of solving linear systems?

Tip:

Always simplify equations fully before attempting to solve, as this can make the process much easier and reduce errors.