Final answer:
The student's problem involves solving a linear equation with two variables by combining like terms and simplifying to find the relation between x and y. This falls under high school mathematics.
Step-by-step explanation:
The student is asking about solving a linear equation in two variables. The equation provided is:
2(y + x) - 3(x - y) = -4.
To solve this, we combine like terms and simplify:
- Distribute the 2 and -3 across the parentheses: 2y + 2x - 3x + 3y.
- Combine like terms: (2y + 3y) + (2x - 3x) = 5y - x.
- Bring all terms to one side of the equation: 5y - x + 4 = 0.
This gives us the simplified form of the equation, which is now ready to be graphed or used to find specific solutions for y in terms of x or vice versa. Remember, when dealing with linear equations, they represent straight lines on a Cartesian plane. The graph of this equation would show the relationship between x and y that satisfies the equation. This content is loaded with necessary steps to manipulate and understand the nature of given linear equations.