Mathemerize

Question :  Form the pair of linear equations for the following problems and find their solution by substitution method. (i)  The difference between two numbers is 26 and one number is three times the other. Find them. (ii)  The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them. (iii)  The coach …

Form the pair of linear equations for the following problems and find their solution by substitution method. Read More »

Solution : We have, 2x + 3y = 11        ….(1) and 2x – 4y = -24        ……(2) From equation (1), we have 2x = 11 – 3y Substituting the value of 2x = 11 – 3y in (2), we get 11 – 3y – 4y = -24 -7y = …

Solve 2x + 3y = 11 and 2x – 4y = -24 and hence find the value of ‘m’ for which y = mx + 3. Read More »

Question : Solve the following pair of linear equations by the substitution method : (i)  x + y = 14    and     x – y = 4 (ii) s – t = 3      and      \(s\over 3\) + \(t\over 2\) = 6 (iii)  3x – y = 3    and    …

Solve the following pair of linear equations by the substitution method : Read More »

Solution : Given Pair of linear equations are : x – y + 1 = 0 ……(i) and 3x + 2y – 12 = 0 …….(ii) first we find points for equation (i), x 0 4 y = x + 1 1 5 Points A B second we find points for equation (ii), x 0 …

Draw the graph of the equation x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region. Read More »

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 »