Question

Please help:

What are the solutions to the system of equations?

x^2 + y^2 = 5
y = 2x

The solution with the smaller x value is (?)
The solution with the larger x value is (?)

Answer 1

(- 1, - 2 ) and (1, 2 )

Explanation:

Given the 2 equations

x² + y² = 5 → (1)

y = 2x → (2)

Substitute y = 2x into (1)

x² + (2x)² = 5

x² + 4x² = 5

5x² = 5 ( divide both sides by 5 )

x² = 1 ( take the square root of both sides )

x = ±
`√(1)` = ± 1

Substitute these values into (2) for corresponding values of y

x = - 1 : y = 2(- 1) = - 2 ⇒ (- 1, - 2 )

x = 1 : y = 2(1) = 2 ⇒ (1, 2 )

The solution with smaller x- value is (- 1, - 2 )

The solution with the larger x value is (1, 2 )