Solve by using the substitution method. Express numbers in exact simplified form. \[ \begin{array}{r}-2 x+5 y=-3 \\ y=-4 x+17\end{array} \] The solution set is \( \{(\square: \square)\} \)

To solve the system of equations using the substitution method, we will substitute the expression for \( y \) from the second equation into the first equation. Starting with the first equation: \[ -2x + 5y = -3 \] Substituting \( y = -4x + 17 \) into the equation: \[ -2x + 5(-4x + 17) = -3 \] Simplifying this, we get: \[ -2x - 20x + 85 = -3 \] \[ -22x + 85 = -3 \] Subtracting 85 from both sides: \[ -22x = -3 - 85 \rightarrow -22x = -88 \] Dividing by -22 gives: \[ x = 4 \] Now, substituting \( x = 4 \) back into the equation for \( y \): \[ y = -4(4) + 17 = -16 + 17 = 1 \] So the solution set is \( \{(4: 1)\} \).