a. \( \begin{array}{l}x=4-2 y \\ 3 x-2 y=4\end{array} \)

To solve the system of equations, we can substitute \( x \) from the first equation into the second. Plugging \( x = 4 - 2y \) into \( 3x - 2y = 4 \) gives us: \[ 3(4 - 2y) - 2y = 4 \] This simplifies to: \[ 12 - 6y - 2y = 4 \] \[ 12 - 8y = 4 \] By rearranging, we find: \[ -8y = 4 - 12 \] \[ -8y = -8 \] Thus, \( y = 1 \). Plugging \( y \) back into the first equation: \[ x = 4 - 2(1) = 2 \] So, the solution is \( (x, y) = (2, 1) \). --- Both equations represent linear relationships, so solving them involves finding where these lines intersect. You can visualize it with a graph; the lines will cross at the coordinates \( (2, 1) \). Graphical representations can make it easier to understand the concept of systems and their solutions. If you apply this in real life, such as in budget planning or project management, these equations can represent resource allocation. Finding the intersection point helps in making decisions about how to optimally distribute limited resources among competing needs.