problem archive
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Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions: \[5x - 8y + 1 = 0\] \[3x - \f... -
Champa went to a 'Sale' to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, "The number of sk... -
Form the pair of linear equations in the following problems, and find their solutions graphically. (i) 10 students of Class X took part in a Mathemati... -
5 pencils and 7 pens together cost ₹ 50, whereas 7 pencils and 5 pens together cost ₹ 46. Find the cost of one pencil and that of one pen. -
On comparing the ratios \(\frac{a_1}{a_2}\), \(\frac{b_1}{b_2}\) and \(\frac{c_1}{c_2}\), find out whether the lines representing the following pairs ... -
On comparing the ratios \(\frac{a_1}{a_2}\), \(\frac{b_1}{b_2}\) and \(\frac{c_1}{c_2}\), find out whether the following pair of linear equations are ... -
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically: (i) \(x + y = 5\) and \(... -
Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden. -
Given the linear equation \(2x + 3y - 8 = 0\), write another linear equation in two variables such that the geometrical representation of the pair so ... -
Draw the graphs of the equations \(x - y + 1 = 0\) and \(3x + 2y - 12 = 0\). Determine the coordinates of the vertices of the triangle formed by these... -
Solve the following pair of equations by substitution method: \(7x - 15y = 2\) \(x + 2y = 3\) -
Solve the following question—Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shal... -
In a shop the cost of 2 pencils and 3 erasers is ₹9 and the cost of 4 pencils and 6 erasers is ₹18. Find the cost of each pencil and each eraser. -
Two rails are represented by the equations x + 2y - 4 = 0 and 2x + 4y - 12 = 0. Will the rails cross each other? -
Solve the following pair of linear equations by the substitution method. (i) $x + y = 14$ $x - y = 4$ -
Solve the following pair of linear equations by the substitution method. (ii) $s - t = 3$ $\frac{s}{3} + \frac{t}{2} = 6$ -
Solve the following pair of linear equations by the substitution method. (iii) $3x - y = 3$ $9x - 3y = 9$ -
Solve the following pair of linear equations by the substitution method. (iv) $0.2x + 0.3y = 1.3$ $0.4x + 0.5y = 2.3$ -
Solve the following pair of linear equations by the substitution method. (v) $\sqrt{2}x + \sqrt{3}y = 0$ $\sqrt{3}x - \sqrt{8}y = 0$ -
Solve the following pair of linear equations by the substitution method. (vi) $\frac{3x}{2} - \frac{5y}{3} = -2$ $\frac{x}{3} + \frac{y}{2} = \frac{13...