Question
Solve the given system of linear equations by inspection y=3/5x-5. y=-3/5x-5 no solution, infinetly many solutions, (-5,0) (0,-5)
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Answered by
GPT 3.5
The system of linear equations is:
1) y = (3/5)x - 5
2) y = (-3/5)x - 5
By inspection, we can immediately see that the slopes of the two equations are opposite reciprocals of each other (3/5 and -3/5). This means that the lines represented by these equations are perpendicular to each other.
Since the lines are perpendicular, they can only intersect at one point. Therefore, there is a unique solution to the system of equations.
To find the point of intersection, we can set the two equations equal to each other:
(3/5)x - 5 = (-3/5)x - 5
By simplifying and rearranging the equation, we get:
(3/5)x + (3/5)x = 0
(6/5)x = 0
x = 0
Substituting this value of x into either of the original equations, we can find the corresponding y-coordinate:
y = (3/5)(0) - 5
y = -5
Therefore, the solution to the system of equations is (0, -5), which corresponds to the point of intersection of the two lines.
1) y = (3/5)x - 5
2) y = (-3/5)x - 5
By inspection, we can immediately see that the slopes of the two equations are opposite reciprocals of each other (3/5 and -3/5). This means that the lines represented by these equations are perpendicular to each other.
Since the lines are perpendicular, they can only intersect at one point. Therefore, there is a unique solution to the system of equations.
To find the point of intersection, we can set the two equations equal to each other:
(3/5)x - 5 = (-3/5)x - 5
By simplifying and rearranging the equation, we get:
(3/5)x + (3/5)x = 0
(6/5)x = 0
x = 0
Substituting this value of x into either of the original equations, we can find the corresponding y-coordinate:
y = (3/5)(0) - 5
y = -5
Therefore, the solution to the system of equations is (0, -5), which corresponds to the point of intersection of the two lines.
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