Solve the system using substitution. \( \left\{\begin{array}{l}5 x-7 y=-58 \\ 3 x+y=-14\end{array}\right. \) One solution: Ono solution Onfinite number of solutions

To solve the system using substitution, let's start with the second equation, \( 3x + y = -14 \). We can express \( y \) in terms of \( x \): \[ y = -14 - 3x. \] Next, we substitute this expression for \( y \) into the first equation: \[ 5x - 7(-14 - 3x) = -58. \] Now, simplify and solve for \( x \): \[ 5x + 98 + 21x = -58 \] \[ 26x + 98 = -58 \] \[ 26x = -58 - 98 \] \[ 26x = -156 \] \[ x = -6. \] Now, substitute \( x = -6 \) back into the equation for \( y \): \[ y = -14 - 3(-6) = -14 + 18 = 4. \] Thus, the solution to the system is \( (x, y) = (-6, 4) \). There is one unique solution! 🎉