Question

Solve the system of equations: x² + y² = 1, y = -4x - 1. Select the correct answer.

1) There is no solution
2) There is exactly one solution
3) There are infinitely many solutions
4) Cannot be determined

Answer 1

To solve the system of equations x² + y² = 1 and y = -4x - 1, substitute the value of y from the second equation into the first equation and solve for x. Then substitute the values of x back into the second equation to find the corresponding values of y.

Step-by-step explanation:

To solve the system of equations x² + y² = 1 and y = -4x - 1, we can substitute the value of y from the second equation into the first equation.

Substituting y = -4x - 1 into x² + y² = 1 gives us the equation x² + (-4x - 1)² = 1.

Simplifying this equation will give us a quadratic equation in terms of x, which we can solve to find the values of x. We can then substitute these values back into the second equation to find the corresponding values of y.