b) \( \left\{\begin{array}{l}4 x-3 y=7 \\ x+1 y=10\end{array}\right. \)

To solve the system of equations, start with the second equation: \( x + y = 10 \), which can be rewritten as \( y = 10 - x \). Substitute this expression for \( y \) into the first equation: \( 4x - 3(10 - x) = 7 \). This simplifies to \( 4x - 30 + 3x = 7 \), leading to \( 7x - 30 = 7 \). Solving for \( x \), you get \( 7x = 37 \) or \( x = \frac{37}{7} \). Plugging \( x \) back into \( y = 10 - x \) gives \( y = 10 - \frac{37}{7} = \frac{70 - 37}{7} = \frac{33}{7} \). Thus, the solution is \( \left( \frac{37}{7}, \frac{33}{7} \right) \). Finding the intersection of the two lines represented by these equations visually can enhance understanding. If we graph them on a coordinate plane, the two lines will cross at the point \( \left( \frac{37}{7}, \frac{33}{7} \right) \). This graphical approach not only helps in visualizing the solution but also illustrates the relationship between the two linear equations, making it easier to conceptualize systems of equations in general.