Solve the system by substitution. \[ \left\{\begin{array}{l}y=5.8 x+17.64 \\ y=-3 x-7\end{array}\right. \]

To solve the system of equations by substitution, we can use the first equation \( y = 5.8x + 17.64 \) and substitute it into the second equation \( y = -3x - 7 \). Starting with the substitution: \[ 5.8x + 17.64 = -3x - 7 \] Now, combine like terms by adding \( 3x \) to both sides: \[ 5.8x + 3x + 17.64 = -7 \] \[ 8.8x + 17.64 = -7 \] Next, isolate \( 8.8x \) by subtracting \( 17.64 \) from both sides: \[ 8.8x = -7 - 17.64 \] \[ 8.8x = -24.64 \] Now, divide both sides by \( 8.8 \) to solve for \( x \): \[ x = \frac{-24.64}{8.8} \approx -2.8 \] Next, substitute \( x \approx -2.8 \) back into the first equation to find \( y \): \[ y = 5.8(-2.8) + 17.64 \] \[ y \approx -16.24 + 17.64 \approx 1.4 \] Thus, the solution to the system is: \[ (x, y) \approx (-2.8, 1.4) \]