Questions: 15.2 x^2+3 y^2=11 x^2+4 y^2=8

Solution Steps

To solve the given system of equations, we can use the method of substitution or elimination. Here, we will use the elimination method to eliminate one of the variables and solve for the other. Once we have one variable, we can substitute it back into one of the original equations to find the second variable.

We start with the following system of equations: \[ \begin{align*}

1. & \quad 15.2 x^{2} + 3 y^{2} = 11 \\
2. & \quad x^{2} + 4 y^{2} = 8 \end{align*} \]

By solving the system, we find the following solutions for the variables \(x\) and \(y\): \[ \begin{align_} (x, y) & = (-0.5882, -1.3833) \\ (x, y) & = (-0.5882, 1.3833) \\ (x, y) & = (0.5882, -1.3833) \\ (x, y) & = (0.5882, 1.3833) \end{align_} \]

Final Answer