Question

X²+y²=100 y-x=2 List the solution or solutions as ordered pairs.

Answer 1

The solutions as ordered pairs are (-8, -6) and (6, 8).

Step-by-step explanation:

The given system of equations is:

• x²+y²=100
• y-x=2

To find the solution or solutions as ordered pairs, we can use the second equation to express y in terms of x and substitute it into the first equation:

y = x + 2

x² + (x + 2)² = 100

Simplify and solve for x:

x² + x² + 4x + 4 = 100

2x² + 4x - 96 = 0

x² + 2x - 48 = 0

(x + 8)(x - 6) = 0

So x can be -8 or 6. Substitute these values back into y = x + 2 to find the corresponding y-values:

For x = -8, y = -8 + 2 = -6

For x = 6, y = 6 + 2 = 8

Therefore, the solutions as ordered pairs are (-8, -6) and (6, 8).