How do you use the substitution method to solve the system of equations 3x + 5y = 3 and x + 2y = 0?

To solve the system of equations using the substitution method, we will follow these steps:

1. Identify the equations:
• Equation 1: 3x + 5y = 3
• Equation 2: x + 2y = 0
2. Rearrange one of the equations to express one variable in terms of the other:
• From Equation 2, we can solve for x:
• x = -2y
3. Substitute this expression into the other equation:
• Now, substitute x = -2y into Equation 1:
• 3(-2y) + 5y = 3
• Simplify the equation:
• -6y + 5y = 3
• -y = 3
• To solve for y, multiply both sides by -1:
• y = -3
4. Substitute this value back to find x:
• Now substitute y = -3 back into the expression for x
• x = -2(-3)
• x = 6
5. State the solution:
• The solution to the system of equations is: (x, y) = (6, -3)