Mathematics
Grade-8
Easy
Question
What is the name of lines when the following equations are drawn on a graph?
![3 x plus 4 y equals 2
6 y plus 8 y equals 4](data:image/png;base64,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)
- Intersecting lines
- Parallel lines
- Coincident lines
- None of the above
Hint:
given two equations of line in the form
A1x + B1y + C1 = 0
A2x + B2y + C2 = 0
then following conditions hold
if ![fraction numerator A 1 over denominator A 2 end fraction equals space fraction numerator B 1 over denominator B 2 end fraction space equals space fraction numerator C 1 over denominator C 2 end fraction space comma space space t h e n space i t space i s space c o i n c i d e n t space
i f space comma space fraction numerator A 1 over denominator A 2 end fraction equals space fraction numerator B 1 over denominator B 2 end fraction space n o t space e q u a l space space fraction numerator C 1 over denominator C 2 end fraction space comma space space t h e n space i t space i s space p a r a l l e l space
e l s e space i f space comma space fraction numerator A 1 over denominator A 2 end fraction space n o t space e q u a l space fraction numerator B 1 over denominator B 2 end fraction space n o t space e q u a l space fraction numerator C 1 over denominator C 2 end fraction space comma space space t h e n space i t space i s space i n t e r s e c t i n g space](data:image/png;base64,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)
The correct answer is: Coincident lines
Given two lines
![3 x plus 4 y equals 2
6 y plus 8 y equals 4](data:image/png;base64,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)
step 1 :
check for conditions
![fraction numerator A 1 over denominator A 2 end fraction equals space fraction numerator B 1 over denominator B 2 end fraction space equals space fraction numerator C 1 over denominator C 2 end fraction space comma space space t h e n space i t space i s space c o i n c i d e n t space
i f space comma space fraction numerator A 1 over denominator A 2 end fraction equals space fraction numerator B 1 over denominator B 2 end fraction space n o t space e q u a l space space fraction numerator C 1 over denominator C 2 end fraction space comma space space t h e n space i t space i s space p a r a l l e l space
e l s e space i f space comma space fraction numerator A 1 over denominator A 2 end fraction space n o t space e q u a l space fraction numerator B 1 over denominator B 2 end fraction space n o t space e q u a l space fraction numerator C 1 over denominator C 2 end fraction space comma space space t h e n space i t space i s space i n t e r s e c t i n g 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)
step 2;
, condition for coincidence holds
So , Given lines are coincident
Related Questions to study
Mathematics
What is the name of lines when the following equations are drawn on a graph?
![space 4 space x minus 6 space y equals 15
space space 2 space x minus 3 space y equals 5](data:image/png;base64,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)
What is the name of lines when the following equations are drawn on a graph?
![space 4 space x minus 6 space y equals 15
space space 2 space x minus 3 space y equals 5](data:image/png;base64,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)
MathematicsGrade-8
Mathematics
What is the slope in the following equation y = 3x + 5?
What is the slope in the following equation y = 3x + 5?
MathematicsGrade-8
Mathematics
The difference of 5 times x and 4 times y is 1. And the difference of 2 times x and y is -2. Find the value of x and y.
The difference of 5 times x and 4 times y is 1. And the difference of 2 times x and y is -2. Find the value of x and y.
MathematicsGrade-8
Mathematics
The sum of two numbers is -4. The sum of 3 times the first number and 4 times the second number is -13. Find the numbers.
The sum of two numbers is -4. The sum of 3 times the first number and 4 times the second number is -13. Find the numbers.
MathematicsGrade-8
Mathematics
The ratio of incomes of two persons is 9:7, and the ratio of their expenditure is 4:3. If each of them manages to save $2000 per month, find their monthly expenditure?
The ratio of incomes of two persons is 9:7, and the ratio of their expenditure is 4:3. If each of them manages to save $2000 per month, find their monthly expenditure?
MathematicsGrade-8
Mathematics
Mary told her daughter, “Seven years ago, I was seven times as old as you were then. Also, three years later from now, I shall be three times as old as you will be.” Find the present ages of Mary and her daughter?
Mary told her daughter, “Seven years ago, I was seven times as old as you were then. Also, three years later from now, I shall be three times as old as you will be.” Find the present ages of Mary and her daughter?
MathematicsGrade-8
Mathematics
The sum of two numbers is 14, and their difference is 2. Find the number.
The sum of two numbers is 14, and their difference is 2. Find the number.
MathematicsGrade-8
Mathematics
Solve the following using the substitution method and find the value of x and y:
6x – 3y = -10
2x – y = -9
Solve the following using the substitution method and find the value of x and y:
6x – 3y = -10
2x – y = -9
MathematicsGrade-8
Mathematics
Solve the following using the substitution method and find the value of x and y:
4x + y = -9
5x – 3y = 10
Solve the following using the substitution method and find the value of x and y:
4x + y = -9
5x – 3y = 10
MathematicsGrade-8
Mathematics
Solve the following using the substitution method and find the value of x and y:
2x + 4y = 16
5x – 3y = -25
Solve the following using the substitution method and find the value of x and y:
2x + 4y = 16
5x – 3y = -25
MathematicsGrade-8
Mathematics
Solve the following using the substitution method and find the value of x and y:
x + 4y = -18
2x + y = -1
Solve the following using the substitution method and find the value of x and y:
x + 4y = -18
2x + y = -1
MathematicsGrade-8
Mathematics
Solve the following using the substitution method and find the value of x and y:
4y = 8
x – 5y = -13
Solve the following using the substitution method and find the value of x and y:
4y = 8
x – 5y = -13
MathematicsGrade-8
Mathematics
Solve the following using the substitution method and find the value of x and y:
x – 5y = 12
x – y = 4
Solve the following using the substitution method and find the value of x and y:
x – 5y = 12
x – y = 4
MathematicsGrade-8
Mathematics
Solve the following using the substitution method and find the value of x and y:
-5x - 4y = 32
2y = -6
Solve the following using the substitution method and find the value of x and y:
-5x - 4y = 32
2y = -6
MathematicsGrade-8
Mathematics
Solve the following using the substitution method and find the value of x and y:
-3y = 12
5x + 5y = -45
Solve the following using the substitution method and find the value of x and y:
-3y = 12
5x + 5y = -45
MathematicsGrade-8