Linear Equation
Question
Q1.
If the point (4,3) lies on the linear equation.
3x - ky = 9,find k.
(a) 1 (b) 2 (c) 3 (d) 4
Solution.
Point (4,3) lies on the linear equation so it will satisfy the equation.
3(4) - k(3) = 9
12 - 3k = 9
-3k = 9 - 12
k = 1
Solution
Q2.
The cost of table is 1/3 of the cost of chair develop linear relationship for this (y = cost of table).
x = 3y
Solution
Q3.
If the point (1,2) lies on the equation 4x - ky = 1 ,find k.
Solution.
1
Solution
Q4.
One side of rectangle lies along the line 4x - 7y + 3 = 0, Two of its vertices are (1,1) and (-2,1),find the equationof side which is
parallel to given line.
(a) 4x + 7y + 15 = 0 (b) 4x - 7y + 15 = 0 (c) 4x - 9y + 3 = 0 (d) 4x - 7y - 15 = 0
Solution.
(b) 4x - 7y + 15 = 0
Point (1,1) lies on the given line. so point (-2,1) lies on the another line which is parallel to given line .
4x - 7y + k = 0
4(-2) - 7(1) + k = 0
-8 - 7 + k = 0
-15 + k = 0
k = 15
Solution
Q5.
A pair of lines is intersecting if
(a) a1/a2 ≠ b1/b2 (b) a1/a2 =ba1ba2
(c) a1/a2 = b1/b2 =c1/c2 (d) None of these
Solution.
(a) a1/a2 ≠ b1/b2
Solution
Q6.
Find the equation of the straight line that passes through (1,2) and perpendicular to the line 6x + 5y + 3 = 0
(a) 6x - 5y + 7 = 0 (b) 5x + 6y + 7 = 0 (c) 5x - 6y + 3 = 0 (d) 5x - 6y + 7 = 0
Solution.
5x - 6y + k = 0
5(1) - 6(2) + k = 0
5 - 12 + k = 0
-7 + k = 0
k = 7
5x - 6y + 7 = 0
Solution
Q7.
Find the value of 'k' for which the system of equations kx + 2y = 5 and 3x + y = 2 has no solution is .
(a) 1/3 (b) 1/6 (c) 3 (d) 6
Solution.
(d) 6
Solution
Q8.
The value of k for which the system of equations x + 2y - 3 = 0 and 5x + ky + 7 = 0 has no solution, is
(a) 10 (b) 6 (c) 3 (d) 1
Solution.
10
Solution
Q9.
The value of k for which the system of equations
2x+3y = 5
4x+ky = 10
has infinite number of solutions, is
(a) 1 (b) 3 (c) 6 (d) 0
Solution.
6
Solution
Q10.
Write the set of values of a and b for which the following system of equations has infinitely many solution .
2x + 3y = 7
2ax + (a + b)y = 28
Solution.
a = 4, b = 8
Solution
