Mathematics
Grade-8
Easy
Question
Check each of the given systems of equations to see if it has a unique solution, infinitely solutions or no solution.
3x + 2y = 6
6x + 4y = 18 solutions of the system
- Unique solution
- Infinite solutions
- No solution
- None of the above
Hint:
use relation
![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](https://lh6.googleusercontent.com/s8qZYYi7jmFM9U_Y_bllz4LNjqvAN3wUB3OFtk_TVqaKhjEjP2QGXO1b26fp89aSrIj0lJhR6Kgeo6RhN-5EB3NovrLel6l0I9AUpHsTg6KHnAqigtXz-BGu59t_l2_lPX8QWW_4kyP0KTb8wpDG9f8)
The correct answer is: No solution
Given lines are
3x + 2y = 6
6x + 4y = 18
Check for their solution
use relation
![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](https://lh6.googleusercontent.com/s8qZYYi7jmFM9U_Y_bllz4LNjqvAN3wUB3OFtk_TVqaKhjEjP2QGXO1b26fp89aSrIj0lJhR6Kgeo6RhN-5EB3NovrLel6l0I9AUpHsTg6KHnAqigtXz-BGu59t_l2_lPX8QWW_4kyP0KTb8wpDG9f8)
Step 1 :
Checking relation
![3 over 6 space equals space fraction numerator 2 over denominator 4 space end fraction space not equal to fraction numerator 6 over denominator 18 space end fraction](data:image/png;base64,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)
step 2 :
so , it satisfies the condition of parallel lines which never meet
SO , GIVEN lines have no solution as they not have any common point
3x + 2y = 6
6x + 4y = 18
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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