Question

What is the solution set of x2(^)+y2(^)=26 and x-y=6

A. {(5,-1),(-5,1)}
B. {(1,5),(5,1)}
C. {(-1,5),(1,5)}
D. {(5,-1),(1,-5)}

Answer 1

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