What are the solutions to the system of equations? x² + y² = 5 and y = 2x?

Solution:

Given, the system of equations are

x² + y² = 5 --- (1)

y = 2x --- (2)

We have to find the solution to the system of equations.

Substitute the value of y in (1)

x² + (2x)² = 5

x² + 4x² = 5

5x² = 5

x² = 5/5

x² = 1

Taking square root,

x = ±1

When x = 1, y = 2(1) = 2

When x = -1, y = 2(-1) = -2

Therefore, the solutions are (1, 2) and (-1, -2).

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What are the solutions to the system of equations? x² + y² = 5 and y = 2x?

Summary:

The solutions to the system of equations x² + y² = 5 and y = 2x are (1, 2) and (-1, -2).