Subtitution is the simplest method to find the solution
First, change x to the value of y from the second equation x - y = 6 x = y + 6
Second, subtitute x with the value of y in the first equation, to find the exact value of y. x² + y² = 26 (y + 6)² + y² = 26 y² + 12y + 36 + y² = 26 2y² + 12y + 36 - 26 = 0 2y² + 12y + 10 = 0 y² + 6y + 5 = 0 (y + 5)(y + 1) = 0 y = -5 or y = -1
Third, we have 2 values for y. We should find the value of x for each y-value For y = -5 x = y + 6 x = -5 + 6 x =1
For y = -1 x = y + 6 x = -1 + 6 x = 5
The solution are (1,-5) and (5,-1). The answer is option d