substitution method: \[ 3 x+2 y=2 \text { and } 5 x-2 y=-18 \]

Solve the system of equations \( 3x+2y=2;5x-2y=-18 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}3x+2y=2\\5x-2y=-18\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{2-2y}{3}\\5x-2y=-18\end{array}\right.\) - step2: Substitute the value of \(x:\) \(5\times \frac{2-2y}{3}-2y=-18\) - step3: Simplify: \(\frac{5\left(2-2y\right)}{3}-2y=-18\) - step4: Multiply both sides of the equation by LCD: \(\left(\frac{5\left(2-2y\right)}{3}-2y\right)\times 3=-18\times 3\) - step5: Simplify the equation: \(10-16y=-54\) - step6: Move the constant to the right side: \(-16y=-54-10\) - step7: Subtract the numbers: \(-16y=-64\) - step8: Change the signs: \(16y=64\) - step9: Divide both sides: \(\frac{16y}{16}=\frac{64}{16}\) - step10: Divide the numbers: \(y=4\) - step11: Substitute the value of \(y:\) \(x=\frac{2-2\times 4}{3}\) - step12: Calculate: \(x=-2\) - step13: Calculate: \(\left\{ \begin{array}{l}x=-2\\y=4\end{array}\right.\) - step14: Check the solution: \(\left\{ \begin{array}{l}x=-2\\y=4\end{array}\right.\) - step15: Rewrite: \(\left(x,y\right) = \left(-2,4\right)\) The solution to the system of equations \(3x+2y=2\) and \(5x-2y=-18\) is \(x=-2\) and \(y=4\).