Answer:
To find the values of x and y in the given equations:
Equation 1: x^2 + y^2 + 6xy + 3x + 5y + 11 = 0
Equation 2: 2x^2 + 4y^2 + 12xy + 9x + 7y + 3 = 0
We can solve this system of equations by using the method of substitution. Here are the steps:
Step 1: Rearrange the equations to isolate one variable in terms of the other.
Let's start with Equation 1. We can rewrite it as:
x^2 + (6y+3)x + (y^2 + 5y + 11) = 0
Step 2: Solve Equation 1 for x.
Using the quadratic formula, x = [-b ± √(b^2 - 4ac)] / (2a), where a, b, and c are the coefficients of the quadratic equation (ax^2 + bx + c = 0), we can substitute the values from Equation 1 into the quadratic formula:
x = [-(6y+3) ± √((6y+3)^2 - 4(1)(y^2 + 5y + 11))] / (2(1))
Simplifying the equation further will give us the value of x in terms of y.
Step 3: Substitute the value of x in Equation 2.
Replace x in Equation 2 with the expression obtained in Step 2. Then simplify the equation to solve for y.
Step 4: Substitute the value of y in Equation 1 to find the corresponding x-value.