Question
How many solutions does the system have? 12x-15y=18 and 4x-5y=6
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Answered by
GPT 3.5
To determine the number of solutions in a system of equations, we need to compare the slopes of the two lines representing the equations.
We can rearrange the first equation, 12x - 15y = 18, to the slope-intercept form: y = (4/5)x - 2/5.
This tells us that the slope of the first line is 4/5.
We can rearrange the second equation, 4x - 5y = 6, to the slope-intercept form: y = (4/5)x - 6/5.
This tells us that the slope of the second line is also 4/5.
Since the slopes of both lines are the same, it means the lines are parallel. Parallel lines never intersect, so they do not have any solution in common. Therefore, the system has no solution.
We can rearrange the first equation, 12x - 15y = 18, to the slope-intercept form: y = (4/5)x - 2/5.
This tells us that the slope of the first line is 4/5.
We can rearrange the second equation, 4x - 5y = 6, to the slope-intercept form: y = (4/5)x - 6/5.
This tells us that the slope of the second line is also 4/5.
Since the slopes of both lines are the same, it means the lines are parallel. Parallel lines never intersect, so they do not have any solution in common. Therefore, the system has no solution.
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