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2x+3y=5,4x+ky=10 find the value of k by infinity many solution |
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Answer» Equation 1: 2x + 3y = 5Equation 2: 4x + ky = 10Both the equations are in the form of :a1x + b1y = c1 & a2x + b2y = c2 where a1 & a2 are the coefficients of xb1 & b2 are the coefficients of yc1 & c2 are the constantsFor the system of linear equations to have infinitely many solutions we must havea1/a2 = b1/b2 = c1/c2 ………(i)According to the problem:a1 = 2, a2 = 4, b1 = 3, b2 = k, c1 = 5, c2 = 10Putting the above values in equation (i) and solving the extreme left and extreme right portion of the equality we get the value of a2/4 = 3/k⇒ 2k = 12 ⇒ k = 6The value of k for which the system of equations has infinitely many solution is k = 6 Given - infinitely many solution =2/4=3/k K=6 |
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