Which ordered pair represents a solution to both equations? Responses A (-5, -1)(-5, -1) B (-1, -5)(-1, -5) C (1, 5)(1, 5) D (-1, 5)
line 1; (-7,-2) (7,-9)
line 2; (5,-2) (-7,-8)
To find the solution that is common to both equations, we need to determine which ordered pair satisfies both equations.
For the first set of points:
Equation of line 1: (-7,-2) and (7,-9)
Slope = (y2 - y1) / (x2 - x1) = (-9 + 2) / (7 + 7) = -7 / 14 = -1/2
Equation of the line: y = mx + b
Using point (-7, -2): -2 = (-1/2)(-7) + b
-2 = 7/2 + b
b = -11/2
Therefore, equation of line 1 is: y = (-1/2)x - 11/2
For the second set of points:
Equation of line 2: (5,-2) and (-7,-8)
Slope = (-8 + 2) / (-7 - 5) = -6 / -12 = 1/2
Equation of the line: y = mx + b
Using point (5, -2): -2 = (1/2)(5) + b
-2 = 5/2 + b
b = -9/2
Therefore, equation of line 2 is: y = (1/2)x - 9/2
Now, we need to find the point that satisfies both equations:
y = (-1/2)x - 11/2
y = (1/2)x - 9/2
Solving for x and y, we find that the point (-5, -1) satisfies both equations.
Therefore, the correct answer is A: (-5, -1)