Consider the system of equations: \( \begin{array}{l}x=-4 y+7 \\ y=\frac{3}{4}\end{array} \)

To solve the system of equations, we first substitute the value of \( y \) from the second equation into the first. Plugging \( y = \frac{3}{4} \) into the first equation gives us: \[ x = -4\left(\frac{3}{4}\right) + 7 \] This simplifies to \( x = -3 + 7 \), which yields \( x = 4 \). Therefore, the solution to the system of equations is \( (4, \frac{3}{4}) \). In this type of linear system, understanding how to manipulate equations is crucial. A common mistake is neglecting to substitute correctly or miscalculating negative signs. Double-checking your arithmetic can save you from unnecessary errors and lead to the right solution every time! A solid foundation in linear equations not only helps in academic settings but also in daily life scenarios like budgeting or project planning. Knowing how to solve these equations assists in making informed decisions based on calculated outcomes!