General Form of a Linear Equation in Two Variables
Trending Questions
A shopkeeper gives books on rent for reading.
She takes a fixed charge for the first two days, and an additional charge for each day thereafter.
Latika paid $\u20b922$for a book kept for six days, while Anand paid $\u20b916$ for the book kept for four days.
Find the fixed charges and the charge for each extra day.
$\u20b913,\u20b92$
$\u20b910,\u20b93$
$\u20b912,\u20b99$
$\u20b914,\u20b95$
From Bangalore bus stand, if we buy 2 tickets to Malleshwaram and 3 tickets to Yeshwanthpur, the total cost is Rs. 46; but if we buy 3 tickets to Malleshwaram and 5 tickets to Yeshwanthpur, then the total cost is Rs. 74. Find the fares from Bangalore bus stand to Malleshwaram and Yeshwanthpur.
Rs. 10 and Rs. 8
Rs. 12 and Rs. 10
Rs. 10 and Rs. 12
Rs. 8 and Rs. 10
Find the value of $k$ for which the following system of linear equations has infinite solutions:
$x+(k+1)y=5\phantom{\rule{0ex}{0ex}}(k+1)x+9y=8k1$
$3$
$1$
$2$
$4$
If 2 is added to the numerator and denominator the fraction becomes 910 and if 3 is subtracted from the numerator and denominator it become 45. Find the fraction.
79.
58.
17.
78.
Determine the truth value of the statement $\mathrm{\forall}x\mathrm{\exists}y(xy=1)$ if the domain for the variables consists of?
The nonzero real numbers.
The nonzero integers.
The positive real numbers.
Rohit can row downstream 32 km in 4 hours and upstream 4km in 1 hour. Find his speed in still water and the speed of the current.
6 km/hr, 2 km/hr
4 km/hr, 4 km/hr
4 km/hr, 2 km/hr
20 km/hr, 4 km/hr
 8 km/hr, 5 km/hr
 8 km/hr, 3 km/hr
 5 km/hr, 3 km/hr
 9 km/hr, 6 km/hr
Select the correct approach for solving a pair of linear equations in 2 variables by elimination method.
i) Add or subtract one equation from the other so that one variable gets eliminated.
ii) Multiply both the equations by any nonzero constant to make the coefficients of one variable (either x or y) numerically equal.
iii) Solve the equation in one variable (x or y) to get its value.
iv) Substitute the value of x (or y) in either of the original equations to get the value of the other variable.
(ii), (i), (iii), (iv)
(i), (ii), (iii), (iv)
(i), (iv), (ii), (iii)
(ii), (i), (iv), (iii)
2√x+3√y=2
4√x−9√y=−1
(where x>0, y>0)
 x=4, y=9
 x=3, y=2
 x=12, y=13
 x=9, y=4
The length of a rectangle is twice the width of it. If the perimeter of the rectangle is 42m. Then the area of the rectangle is _____ .
108 m^{2}
98 m^{2}
224 m^{2}
63 m^{2}
If y = 12 (3x+7) is written in the form ax + by + c = 0, then the values of b is 
3
2
5
7
The linear equation 2x  5y = 7 has:
A) A unique solution
B) Two solution
C) Infinitely many solutions
D) No solution
 (0, 3)
(3, 0)
 (2, 0)
 (0, 2)
Compare the given linear equation 2y=5x+7 with its standard form ax+by+c=0.
Which of the following is the possible value of 'c' for the given equation?
7
1/2
2
7/2
A man can row 40 km upstream and 55 km downstream in 13 hours. He can also row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the boat in still water and the speed of the current.
8 km/hr, 5 km/hr
8 km/hr, 3 km/hr
5 km/hr, 3 km/hr
9 km/hr, 6 km/hr
Any equation which can be put in the form $ax+by+c=0$ where are $a,b,c$ are $\overline{)\left(P\right)}$ and $a$ and $b$ are not both $\overline{)\left(Q\right)}$ , is called linear equation in $\overline{)\left(R\right)}$ .
$\left(P\right)$constants, $\left(Q\right)$zero , $\left(R\right)$three variables
$\left(P\right)$constants, $\left(Q\right)$real number , $\left(R\right)$three variables
$\left(P\right)$real number, $\left(Q\right)$zero , $\left(R\right)$two variables
$\left(P\right)$variables, $\left(Q\right)$constants , $\left(R\right)$two variables
Solve
3x + 2y = 36
5x + 4y = 64

2
7
If the linear equation y = 7x  4 is written in standard form, the standard form being ax +by +c =0, then what is the value of a, b and c?
7, 1, 4
none of these
7, 1, 4
7, 1, 4
The conditions for ax+by+c=0 to be a linear equation in two variables (x, y) are
a=0 and b=0
a≠0 and b≠0
a can be zero but not b
b can be 0 but not a
If the linear equation y = 7x  4 is written in the standard form ax +by +c =0, then what are the values of a, b and c?
7, 1, 4
7, 1, 4
7, 1, 4
none of these
 40, 20
 40, 30
 50, 30
 None of these
It takes 3 hours for a boat to travel 27 km upstream and the same boat can travel 30 km downstream in 2 hours. The speed of the current is 12 km/hr
True
False
The cost of tickets for a movie show was ₹162 for 12 children and 3 adults and was ₹ 122 for 8 children and 3 adults. The ticket cost for each child is ₹10 and each adult is ₹14.
False
True
If Nishu can swim downstream at $6km/h$ and upstream at $2km/h$. What is his speed in still water?
Solve the following pair of equations:
1x+3y=1
6x−12y=2
(Where x≠0, y≠0)
 x=53, y=152
 x=3, y=11
 x=4, y=9
 x=35, y=73
What will you substitute to make the following equation a linear equation?
1x + 3y = 1
1/x as p and 1/y as q
Option A or Option B
None of the above
x as 1/p and y as 1/q
Which one of the following options is true, and why?
y=3x+5 has
(i) a unique solution
(ii) only two solutions
(iii) infinitely many solutions
Points A and B are 90 km apart on a highway. A car starts from A and another from B at the same time. If they travel in the same direction they meet in 9 hours and if they travel in opposite directions they meet in 97 hours. Speed of car starting from point A is:
90 km/hr
40 km/hr
220 km/hr
30 km/hr
A boat covers a distance of 32 km upstream and 36 km downstream in 7 hours. It also covers a distance of 40 km upstream and 48 km downstream in 9 hours. Find the speed of the boat in still water and that of the stream.
44 km/hr, 8 km/hr
14 km/hr, 5 km/hr
6 km/hr, 4 km/hr
10 km/hr, 2 km/hr