1. \( 4 x-5 y=-10 \) 2. \( -2 x+6 y=-6 \) 3. \( -4 x+5 y=0 \) 4. \( x+3 y=-3 \) 5. \( x+5 y=10 \)

Solve the system of equations \( 4x-5y=-10;-2x+6y=-6;-4x+5y=0;x+3y=-3;x+5y=10 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}4x-5y=-10\\-2x+6y=-6\\-4x+5y=0\\x+3y=-3\\x+5y=10\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}4x-5y=-10\\-2x+6y=-6\\-4x+5y=0\\x=-3-3y\\x+5y=10\end{array}\right.\) - step2: Substitute the value of \(x:\) \(\left\{ \begin{array}{l}4\left(-3-3y\right)-5y=-10\\-2\left(-3-3y\right)+6y=-6\\-4\left(-3-3y\right)+5y=0\\-3-3y+5y=10\end{array}\right.\) - step3: Simplify: \(\left\{ \begin{array}{l}-12-17y=-10\\6+12y=-6\\12+17y=0\\-3+2y=10\end{array}\right.\) - step4: Solve the equation: \(\left\{ \begin{array}{l}y=-\frac{2}{17}\\6+12y=-6\\12+17y=0\\-3+2y=10\end{array}\right.\) - step5: Substitute the value of \(y:\) \(\left\{ \begin{array}{l}6+12\left(-\frac{2}{17}\right)=-6\\12+17\left(-\frac{2}{17}\right)=0\\-3+2\left(-\frac{2}{17}\right)=10\end{array}\right.\) - step6: Simplify: \(\left\{ \begin{array}{l}\frac{78}{17}=-6\\10=0\\-\frac{55}{17}=10\end{array}\right.\) - step7: Calculate: \(\left\{ \begin{array}{l}x \in \varnothing \\y \in \varnothing \end{array}\right.\) - step8: Rewrite: \((x, y) \in \varnothing\) The system of equations has no solution.