Substitute y = x - 1 into x² + y² = 25:
x² + (x - 1)² = 25
Simplifying:
2x² - 2x - 24 = 0
x² - x - 12 = 0
Factoring:
(x - 4)(x + 3) = 0
So x = 4 or x = -3.
Substituting each value into y = x - 1 gives y = 3 for x = 4, and y = -4 for x = -3.
Therefore, the points of intersection are (4, 3) and (-3, -4), which corresponds to option b.
The equation x² + y² = 25 defines a circle with center at the origin and radius 5. The line y = x - 1 passes
through the circle. Using the substitution method, find the point(s) at which the circle and the line intersect.
a. (4, 3) and (–4, –3) c. (4, –3) and (–3, 4)
b. (3, 4) and (–3, –4) d. no solution
1 answer
1 answer