Question

Solve the system of equations. {x²+y²=8 {y=x+2

Answer 1

To solve the system of equations, substitute the expression for y in the first equation, simplify and combine like terms to get a quadratic equation. Factor the equation, solve for x and substitute the values into the second equation to find the corresponding y-values. The solutions are (1,3) and (-2,0).

Step-by-step explanation:

To solve the system of equations:

{x²+y²=8

{y=x+2

1. Substitute the expression for y in the first equation:

• x² + (x+2)² = 8

Simplify the equation:

• x² + x² + 4x + 4 = 8

Combine like terms:

• 2x² + 4x - 4 = 0

Factor the quadratic equation (can be done using the quadratic formula or factoring method):

• (2x - 2)(x + 2) = 0

Set each factor equal to zero and solve for x:

• 2x - 2 = 0 or x + 2 = 0
• 2x = 2 or x = -2
• x = 1 or x = -2

Substitute the values of x into the second equation to solve for y:

• For x = 1: y = 1 + 2 = 3
• For x = -2: y = -2 + 2 = 0

The solutions to the system are (1,3) and (-2,0).