What is the solution set of x2(^)+y2(^)=26 and x-y=6 a. {(5,-,1)} b. {(1,,1)} c. {(-1,,5)} d. {(5,-,-5)}

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

Is it multiple choice