For what values of a and b the following equations have infinite solutions 2x+3y=7
2x + 3y -7 = 0 Show
(a - b)x + (a + b)y - 3a + b - 2 = 0 Here `a_1 = 2, b_1 = 3,c_1 = -7` `a_2 = (a - b), b_2 = (a + b), c_2 = -(3a + b - 2)` `a_1/a_2 = 2/(a - b), b_1/b_2 = 3/(a + b), c_1/c_2 = (-7)/(-(3a + b - 2)) = (-7)/(3a + b - 2)` For the equation to have infinitely many solutions, we have: `a_1/a_2 = b_1/b_2 = c_1/c_2` `2/(a - b) = 7/(3a + b -2)` 6a + 2b - 4 = 7a - 7b a- 9b = -4 ......(1) `2/(a -b) = 3/(a + b)` a - 5b = 0 .....(2) Subtracting (1) from (2), we obtain 4b = 4 b = 1 Substituting the value of b in equation (2), we obtain a - 5 x 1 = 0 a = 5 Thus, the values of a and b are 5 and 1 respectively.
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Answer Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams. Related Videos587173932 0 7.7 K 3:27 For what values of a and b does the following pair of linear equations have infinite number of solution ?
405975365 0 4.0 K 5:30 a ಮತ್ತು b ಗಳ ಯಾವ ಬೆಲೆಗಳಿಗೆ ಕೆಳಗೆ ನೀಡಿದ ರೇಖಾತ್ಮಕ ಸಮೀಕರಣಗಳ ಜೋಡೆಯು ಅಪರಿಮಿತ ಸಂಖ್ಯೆಯ ಪರಿಹಾರಗಳನ್ನು ಹೊಂದಿರುತ್ತದೆ? `2x + 3y= 7` `(a - b )x +(a +b)y =3a +b -2` 642722722 0 8.1 K 6:07 For what values of a and b does the following pair of linear equations have infinitely many solutions ? 94832606 0 3.4 K 2:27 a और b के किन मोनो के लिये निम्न रेखिक समीकरणो के युग्म के अपरिमित रूप से
अनके हल होंगे ? 643582161 0 4.7 K 4:28 a ਅਤੇ b ਦੇ ਕਿਹੜੇ ਮੁੱਲਾਂ ਦੇ ਲਈ, ਹੇਠਾਂ ਦਿੱਤੇ ਰੇਖੀ ਸਮੀਕਰਣਾਂ ਦੇ ਜੋੜੇ ਦੇ ਅਣਗਿਣਤ ਰੂਪ ਵਿੱਚ ਅਨੇਕ ਹੱਲ ਹੋਣਗੇ ? 2x+3y=7 (a-b)x+(a+b)y=3a+b-2 642722688 0 9.6 K 4:44 For which values of a and b does the following pair of linear
equations have an infinite number of solutions? Show More Comments Add a public comment... Follow Us: Popular Chapters by Class: Class 6 AlgebraBasic Geometrical IdeasData HandlingDecimalsFractions Class 7 Algebraic ExpressionsComparing QuantitiesCongruence of TrianglesData HandlingExponents and Powers Class 8 Algebraic Expressions and IdentitiesComparing QuantitiesCubes and Cube RootsData HandlingDirect and Inverse Proportions Class 9 Areas of Parallelograms and TrianglesCirclesCoordinate GeometryHerons FormulaIntroduction to Euclids Geometry Class 10 Areas Related to CirclesArithmetic ProgressionsCirclesCoordinate GeometryIntroduction to Trigonometry Class 11 Binomial TheoremComplex Numbers and Quadratic EquationsConic SectionsIntroduction to Three Dimensional GeometryLimits and Derivatives Class 12 Application of DerivativesApplication of IntegralsContinuity and DifferentiabilityDeterminantsDifferential Equations Privacy PolicyTerms And Conditions Disclosure PolicyContact Us For what value of k will the following equations have infinitely many solutions 2x 3y 7?Therefore, the given system of equations will have infinitely many solutions, if k=7.
How can you tell if an equation has infinite solutions?Equations with an infinite number of solutions
Some equations have infinitely many solutions. In these equations, any value for the variable makes the equation true. You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself.
For which values of A and B does the following pair of linear infinite number of solutions?For which values of a and b does the following pair of linear equations have an infinite number of solutions? Thus at a = 5 and b = 1 the given equations will have infinite solutions.
For which values of A and B does the following pair of the linear equation have an infinite number of solutions 2x 3y 7 2ax ay 28 by?Therefore for infinite number of solutions a=4 and b=8.
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