Linear Equation in Two Variables Questions

Question : Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is : (i) intersecting lines (ii) parallel lines (iii) coincident lines Solution : The given linear equation is 2x + 3y – 8 = 0 …

Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is : Read More »

Solution : Let x be the length of garden and y be its width. Then, According to question, perimeter = 2(length +width) = 2(x + y) Therefore, half perimeter = (x + y) But it is given as 36 \(\therefore\) (x + y) = 36 Also, x = y + 4 Now, we form the …

Half the perimeter of rectangle garden, whose length is 4m more than its width, is 36 cm. Find the dimensions of the garden. Read More »

Question : Which of the following pairs of linear equations are consistent obtain the solution in such cases graphically. (i) x + y = 5, 2x + 2y = 10 (ii) x – y = 8, 3x – 3y = 10 (iii) 2x + y – 6 = 0, 4x – 2y – 4 = …

Which of the following pairs of linear equations are consistent obtain the solution in such cases graphically. Read More »

Question : On comparing the ratios \(a_1\over a_2\), \(b_1\over b_2\) and \(c_1\over c_2\), find out whether the following pair of linear equations are consistent, or inconsistent. (i)  3x + 2y = 5; 2x – 3y = 7 (ii)  2x – 3y = 8; 4x – 6y = 9 (iii)  \(3\over 2\)x + \(5\over 3\)y = …

On comparing the ratios \(a_1\over a_2\), \(b_1\over b_2\) and \(c_1\over c_2\), find out whether the following pair of linear equations are consistent, or inconsistent. Read More »

Question : On comparing the ratios \(a_1\over a_2\), \(b_1\over b_2\) and \(c_1\over c_2\), find out whether the lines representing the following pair of linear equations intersect at a point, are parallel of coincide. (i) 5x – 4y + 8 = 0; 7x + 6y – 9 = 0 (ii) 9x + 3y + 12 = …

On comparing the ratios \(a_1\over a_2\), \(b_1\over b_2\) and \(c_1\over c_2\), find out whether the lines representing the following pair of linear equations intersect at a point, are parallel of coincide. Read More »

Question : From the pair of linear equations in the following problems, and find their solution graphically. (i) 10 students of class X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz. …

From the pair of linear equations in the following problems, and find their solution graphically. Read More »

Question : The cost of 2 kg apples and 1 kg grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and graphically. Solution : Let us denote the cost of 1 kg …

The cost of 2 kg apples and 1 kg grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Read More »

Question : The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 2 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically. Solution : Let us denote the set of one bat by Rs x and one ball …

The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 2 more balls of the same kind for Rs 1300. Read More »

Question : Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically. Solution : Let the present age of father be x years …

Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Read More »