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Check graphically whether the pair of equations 3x – 2y + 2 = 0 and 3/2x – y + 3 = 0,
is consistent. Also find the coordinates of the points where the graphs of the equations
meet the Y-axis.?
is consistent. Also find the coordinates of the points where the graphs of the equations
meet the Y-axis.?
Most Upvoted Answer
Check graphically whether the pair of equations 3x – 2y + 2 = 0 and 3/...
Consistency of the Equations:
To check the consistency of the equations 3x – 2y + 2 = 0 and 3/2x – y + 3 = 0, we need to graphically represent them on a coordinate plane. If the graphs of the two equations intersect at a point, then the system is consistent.
Graphical Representation:
To graph the equations, we first need to find their y-intercepts. To find the y-intercept, we set x = 0 in each equation and solve for y.
For the first equation:
3(0) - 2y + 2 = 0
-2y + 2 = 0
-2y = -2
y = 1
So, the y-intercept of the first equation is (0, 1).
For the second equation:
3/2(0) - y + 3 = 0
-y + 3 = 0
-y = -3
y = 3
So, the y-intercept of the second equation is (0, 3).
Now, plot these points on a graph and draw the lines representing the equations. If the lines intersect at a point, then the system is consistent.
Conclusion:
After graphing the equations, if the lines intersect at a single point, then the system is consistent, and there is a unique solution to the system of equations. If the lines are parallel, then the system is inconsistent, and there is no solution to the system of equations.
To check the consistency of the equations 3x – 2y + 2 = 0 and 3/2x – y + 3 = 0, we need to graphically represent them on a coordinate plane. If the graphs of the two equations intersect at a point, then the system is consistent.
Graphical Representation:
To graph the equations, we first need to find their y-intercepts. To find the y-intercept, we set x = 0 in each equation and solve for y.
For the first equation:
3(0) - 2y + 2 = 0
-2y + 2 = 0
-2y = -2
y = 1
So, the y-intercept of the first equation is (0, 1).
For the second equation:
3/2(0) - y + 3 = 0
-y + 3 = 0
-y = -3
y = 3
So, the y-intercept of the second equation is (0, 3).
Now, plot these points on a graph and draw the lines representing the equations. If the lines intersect at a point, then the system is consistent.
Conclusion:
After graphing the equations, if the lines intersect at a single point, then the system is consistent, and there is a unique solution to the system of equations. If the lines are parallel, then the system is inconsistent, and there is no solution to the system of equations.
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Check graphically whether the pair of equations 3x – 2y + 2 = 0 and 3/2x – y + 3 = 0, is consistent. Also find the coordinates of the points where the graphs of the equations meet the Y-axis.?
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Check graphically whether the pair of equations 3x – 2y + 2 = 0 and 3/2x – y + 3 = 0, is consistent. Also find the coordinates of the points where the graphs of the equations meet the Y-axis.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Check graphically whether the pair of equations 3x – 2y + 2 = 0 and 3/2x – y + 3 = 0, is consistent. Also find the coordinates of the points where the graphs of the equations meet the Y-axis.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Check graphically whether the pair of equations 3x – 2y + 2 = 0 and 3/2x – y + 3 = 0, is consistent. Also find the coordinates of the points where the graphs of the equations meet the Y-axis.?.
Check graphically whether the pair of equations 3x – 2y + 2 = 0 and 3/2x – y + 3 = 0, is consistent. Also find the coordinates of the points where the graphs of the equations meet the Y-axis.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Check graphically whether the pair of equations 3x – 2y + 2 = 0 and 3/2x – y + 3 = 0, is consistent. Also find the coordinates of the points where the graphs of the equations meet the Y-axis.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Check graphically whether the pair of equations 3x – 2y + 2 = 0 and 3/2x – y + 3 = 0, is consistent. Also find the coordinates of the points where the graphs of the equations meet the Y-axis.?.
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