Final Answer:
The equivalent system of equations for the given vector equation is: x - 2y = 6 and 3x + 4y = 4.
Step-by-step explanation:
A system of equations is a collection of two or more equations containing the same set of unknowns. A vector equation is a representation of an equation in vector form. To find the equivalent system of equations for the given vector equation, we need to first identify the components of the vector equation. The given vector equation is represented as Ax + By = C.
Here, A = x, B = -2y, and C = 6. We can then create a system of equations from the given vector equation. To do this, we first write the two equations as x = C - By and 3x + 4y = C. Substituting the values for A, B, and C in these two equations, we get x = 6 - (-2y) and 3x + 4y = 4. Simplifying the first equation, we get x - 2y = 6. Thus, the equivalent system of equations for the given vector equation is: x - 2y = 6 and 3x + 4y = 4.