Determine, algebraically, the vertices of the triangle formed by the lines 3x – y = 3 2x – 3y = 2 x + 2y = 8 3x – y = 2 …(1) 2x -3y = 2 …(2) x + 2y = 8 …(3) Let the equations of the line (1), (2) and (3) represent the side... View Article
The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box. Given The cost of 4 pens and 4 pencil boxes = Rs 100 Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Find out We... View Article
Draw the graphs of the equations x = 3, x = 5 and 2x – y – 4 = 0. Also find the area of the quadrilateral formed by the lines and the x-axis. Solution Given equation of lines x = 3, x = 5 and 2x-y-4 = 0. Table for line 2x – y – 4 = 0 is tabulated below x 0 2... View Article
Determine, graphically, the vertices of the triangle formed by the lines y = x, 3y = x, x + y = 8 Solution Given linear equations are y = x …(i) 3y = x …(ii) and x + y = 8 …(iii) Table for line y = x is tabulated... View Article
Graphically, solve the following pair of equations: 2x + y = 6 2x – y + 2 = 0 Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis. Solution Given equations are 2x + y = 6 2x – y + 2 = 0 Table for equation 2x + y – 6 = 0, For x = 0 y = 6 and for y = 0,... View Article
Find the values of x and y in the following rectangle [see Figure]. Solution: By the property of rectangel we know that Lengths are equal, i.e., CD = AB Hence, x + 3y = 13 …(i) Breadth are equal,... View Article
If 2x + y = 23 and 4x – y = 19, find the values of 5y – 2x and y/x – 2. Given Given pair of linear equations is 2x + y = 23 …(i) 4x – y = 19 …(ii) Find out We have to determine the values of... View Article
Write a pair of linear equations which has the unique solution x = – 1, y =3. How many such pairs can you write? Solution Condition for the pair of system to have unique solution a1/a2 ≠ b1/b2 Let us assume the equations be, a1x + b1y +... View Article
Two straight paths are represented by the equations x – 3y = 2 and -2x + 6y = 5.Check whether the paths cross each other or not. Given Given pair of linear equations is x – 3y – 2 = 0 …(i) -2x + 6y – 5 = 0 …(ii) Find out We have to... View Article
Find the value(s) of p and q in the following pair of equations: 2x + 3y = 7 and 2px + py = 28 – qy, if the pair of equations have infinitely many solutions. Given Given pair of linear equations is 2x + 3y = 7 2px + py = 28 – qy or 2px + (p + q)y – 28 = 0 Find out We have to... View Article
Find the value(s) of p in the following pair of equations: 2x + 3y – 5 = 0 and px – 6y – 8 = 0, if the pair of equations has a unique solution. Given Given pair of linear equations is 2x + 3y – 5 = 0 px – 6y – 8 = 0 Find out We have to determine the value of p in... View Article
Find the value(s) of p in the following pair of equations: – 3x + 5y = 7 and 2px – 3y = 1, if the lines represented by these equations are intersecting at a unique point. Given Given pair of linear equations is – 3x + 5y = 7 2px – 3y = 1 Find out We have to determine the value of p in the given... View Article
Find the value(s) of p in the following pair of equations: – x + py = 1 and px – y = 1, if the pair of equations has no solution. Given Given pair of linear equations is – x + py = 1 …(i) px – y – 1 = 0 …(ii) Find out We have to determine the... View Article
Find the value(s) of p in the following pair of equations: 3x – y – 5 = 0 and 6x – 2y – p = 0, if the lines represented by these equations are parallel. Given Given pair of linear equations is 3x – y – 5 = 0 …(i) 6x – 2y – p = 0 …(ii) Find out We have to... View Article
For which values of a and b, will the following pair of linear equations have infinitely many solutions? x + 2y = 1 (a – b)x + (a + b)y = a + b – 2 Given x + 2y = 1 (a – b)x + (a + b)y = a + b – 2 Find out We have to... View Article
For which value(s) of k will the pair of equations kx + 3y = k – 3 12x + ky = k have no solution? Solution The given pair of linear equations is kx + 3y = k – 3 …(1) 12x + ky = k …(2) On comparing the equations (1) and... View Article
For which value(s) of λ , do the pair of linear equations λx + y = λ2 and x + λy = 1 have (i) no solution? (ii) infinitely many solutions? (iii) a unique solution? Solution: The given pair of linear equations is λx + y = λ2 and x + λy = 1 a1 = λ, b1= 1, c1 =... View Article
Are the following pair of linear equations consistent? Justify your answer. (i) -3x- 4y = 12 4y + 3x = 12 (ii) (3/5)x – y = ½ (1/5)x – 3y= 1/6 (iii) 2ax + by = a ax + 2by – 2a = 0; a, b ≠0 (iv) x + 3y = 11 2 (2x + 6y) = 22 Solution: We know that Conditions for pair of linear equations to be consistent are: a1/a2 ≠ b1/b2. [unique solution]... View Article
Do the following equations represent a pair of coincident lines? Justify your answer. (i) 3x + 1/7y = 3 7x + 3y = 7 (ii) -2x – 3y = 1 6y + 4x = – 2 (iii) x/2 + y + 2/5 = 0 4x + 8y + 5/16 = 0 Solution We know that the condition for coincident lines, a1/a2 = b1/b2 = c1/c2; (i) 3x + 1/7y = 3 7x + 3y = 7 No. The given pair... View Article
Do the following pair of linear equations have no solution? Justify your answer. (i) 2x + 4y = 3 12y + 6x = 6 (ii) x = 2y y = 2x (iii) 3x + y – 3 = 0 2x + 2/3y = 2 Solution We know that the condition for no solution is a1/a2 = b1/b2 ≠ c1/c2 (parallel lines) (i) 2x + 4y = 3... View Article
