The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be ₹x and that of a pen to be ₹y.)
x − 2y = 0
Express the following linear equations in the form \(ax + by + c = 0\) and indicate the values of \(a, b, c\) in each case:
(i) \(2x + 3y = 9.35\)
(ii) \(x - \dfrac{y}{5} - 10 = 0\)
(iii) \(-2x + 3y = 6\)
(iv) \(x = 3y\)
(v) \(2x = -5y\)
(vi) \(3x + 2 = 0\)
(vii) \(y - 2 = 0\)
(viii) \(5 = 2x\)
(i) \(2x + 3y - 9.35 = 0;\ a = 2,\ b = 3,\ c = -9.35\)
(ii) \(x - \dfrac{y}{5} - 10 = 0;\ a = 1,\ b = -\dfrac{1}{5},\ c = -10\)
(iii) \(-2x + 3y - 6 = 0;\ a = -2,\ b = 3,\ c = -6\)
(iv) \(x - 3y + 0 = 0;\ a = 1,\ b = -3,\ c = 0\)
(v) \(2x + 5y + 0 = 0;\ a = 2,\ b = 5,\ c = 0\)
(vi) \(3x + 0y + 2 = 0;\ a = 3,\ b = 0,\ c = 2\)
(vii) \(0x + 1y - 2 = 0;\ a = 0,\ b = 1,\ c = -2\)
(viii) \(-2x + 0y + 5 = 0;\ a = -2,\ b = 0,\ c = 5\)
Which one of the following options is true, and why?
For the equation \(y = 3x + 5\):
(i) a unique solution
(ii) only two solutions
(iii) infinitely many solutions
(iii), because for every value of x, there is a corresponding value of y and vice-versa.
Write four solutions for each of the following equations:
(i) \(2x + y = 7\)
(ii) \(\pi x + y = 9\)
(iii) \(x = 4y\)
(i) (0, 7), (1, 5), (2, 3), (4, -1)
(ii) (1, 9 - \(\pi\)), (0, 9), (-1, 9 + \pi), \(\left(\dfrac{9}{\pi}, 0\right)\)
(iii) (0, 0), (4, 1), (-4, 1), \(\left(2, \dfrac{1}{2}\right)\)
Check which of the following are solutions of the equation \(x - 2y = 4\) and which are not:
(i) (0, 2)
(ii) (2, 0)
(iii) (4, 0)
(iv) \((\sqrt{2}, 4\sqrt{2})\)
(v) (1, 1)
(i) No
(ii) No
(iii) Yes
(iv) No
(v) No
Find the value of k, if \(x = 2, y = 1\) is a solution of the equation \(2x + 3y = k\).
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