Question
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
minus, x, plus, 6, y, equals, minus, 7
−x+6y=
−7
minus, 5, x, plus, 12, y, equals, minus, 17
−5x+12y=
−17
minus, x, plus, 6, y, equals, minus, 7
−x+6y=
−7
minus, 5, x, plus, 12, y, equals, minus, 17
−5x+12y=
−17
Answers
GPT 3.5
To determine if the system of equations has no solutions, infinitely many solutions, or exactly one solution, we can put the equations into slope-intercept form (y = mx + b) and compare the slopes.
The first equation can be rearranged as:
- x + 6y = -7
6y = x - 7
y = (1/6)x - 7/6
The second equation can be rearranged as:
-5x + 12y = -17
12y = 5x - 17
y = (5/12)x - 17/12
The slope of the first equation is 1/6 and the slope of the second equation is 5/12.
Since the slopes are not equal, the system of equations has exactly one solution.
The first equation can be rearranged as:
- x + 6y = -7
6y = x - 7
y = (1/6)x - 7/6
The second equation can be rearranged as:
-5x + 12y = -17
12y = 5x - 17
y = (5/12)x - 17/12
The slope of the first equation is 1/6 and the slope of the second equation is 5/12.
Since the slopes are not equal, the system of equations has exactly one solution.