If 2x + y = 23 and 4x – y = 19, find the values of 5y – 2x and y/x -2
Write a pair of linear equations which has the unique solution x = – 1, y =3. How many such pairs can you write?
Two straight paths are represented by the equations x – 3y = 2 and –2x + 6y = 5. Check whether the paths cross each other or not.
Two straight paths are represented by the equations x – 3y = 2 and –2x + 6y = 5. Check whether the paths cross each other or not.
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
For which value(s) of k will the pair of equations
kx + 3y = k – 3
12x + ky = k
have no solution?
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?
Draw the graphs of the pair of linear equations x – y + 2 = 0 and 4x – y – 4 = 0. Calculate the area of the triangle formed by the lines so drawn and the x-axis.
Solve the following pair of linear equations:
21x + 47y = 110
47x + 21y = 162
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