# Linear Equation in 2 Variables

## Trending Questions

**Q.**

The sum of distinct values of $\lambda $ for which the system of equations

$\left(\lambda -1\right)x+\left(3\lambda +1\right)y+2\lambda z=0\phantom{\rule{0ex}{0ex}}\left(\lambda -1\right)x+\left(4\lambda -2\right)y+\left(\lambda +3\right)z=0\phantom{\rule{0ex}{0ex}}2x+\left(3\lambda +1\right)y+3\left(\lambda -1\right)z=0$

has no solutions is

**Q.**

How many linear equations can be satisfied by x = 2 and y = 3 ?

(a) only one

(b) only two

(c) only three

(d) infinitely many

**Q.**

If the system of equations

$x+y+z=2\phantom{\rule{0ex}{0ex}}2x+4y\u2013z=6\phantom{\rule{0ex}{0ex}}3x+2y+\lambda z=\mu $

has infinitely many solutions, then

$\lambda -2\mu =-5$

$2\lambda +\mu =14$

$\lambda +2\mu =14$

$2\lambda -\mu =5$

**Q.**

Who introduced the word polynomial?

**Q.**

Solve** :**

$2x-3=x+2$

**Q.**

Factorize the following expression: ${x}^{4}-{(y+z)}^{4}$.

**Q.**

If the system of equations

$x-2y+3z=9\phantom{\rule{0ex}{0ex}}2x+y+z=b\phantom{\rule{0ex}{0ex}}x-7y+az=24,$

has infinitely many solutions, then $a-b$ is equal to:

**Q.**

The taxi fare in a city is as follows: For the first kilometre , the fare is RS. 20 and for the subsequent distance it is Rs.6 per km. Taking x km as the distance covered and RS. y as the total fare, write a linear equation for this information in the form of as+by+c=0 and indicate the values of a, b and c.

**Q.**Question 9 (v)

Solve the following pair of equations 43x + 67y = - 24 and 67x + 43y = 24.

**Q.**

A linear equation in two variables x and y is of the form ax + by + c = 0, where

(a) a≠0, b≠0.

(b) a≠0, b=0

(c) a=0, b≠0

(d) a = 0, c = 0

**Q.**

Find the equation of the line passing through the point $(2,3)$ and having slope $3$.

**Q.**

The cost of ball pen is Rs 5 less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.

**Q.**

cost of 1 pen is Rs.x and that of 1 pencil is Rs.y.cost of 2 pens and 3 pencils together is Rs.18.write a linear equation to represent this information.

**Q.**

The linear equation 3x - 5y = 15 has

(a) a unique solution

(b) two solutions

(c) infinitely many solutions

(d) no solution

**Q.**

Express each of the following equations in the form ax + by + c = 0 and indicate the values of a, b, c in each case.

(i) 3x + 5y = 7.5

(ii) 2x−y5+6=0

(iii) 3y - 2x = 6

(iv) 4x = 5y

(v)x5−y6=1

(vi) √2x+√3y=5

**Q.**

The number of girls x in a class is 5 less than twice the number of boys y of the same class. The linear equation in two variables for this information is

2x - y = 5

x + 2y = -5

x + 5 = 2y

2y - x = -5

**Q.**

The sum of the digits of a two-digit number is 7. If the number formed by interchanging the digits is less than the original number by 27, then find the original number.

43

61

52

25

**Q.**

The sum of three consecutive numbers is $66$ .Find the numbers .

**Q.**Question 14

The perpendicular bisector of a line segment joining points A(1, 5) and B(4, 6) cuts Y-axis at

(A) (0, 13)

(B) (0, –13)

(C) (0, 12)

(D) (13, 0)

**Q.**

The value of ${\left(1+i\right)}^{8}+{\left(1-i\right)}^{8}$ is

$16$

$-16$

$32$

$-32$

**Q.**

If $X$ and $Y$ are two non-empty sets, where $f:X\to Y$is function is defined such that $f\left(C\right)=\left\{f\left(x\right):x\in C\right\}$ for $C\subseteq X$ and ${f}^{-1}\left(D\right)=\left\{x:f\left(x\right)\in D\right\}$for $D\subseteq Y$, for any $A\subseteq Y$ and $B\subseteq Y$, then

${f}^{-1}\left(f\left(A\right)\right)=A$

${f}^{-1}\left(f\left(A\right)\right)=A$ only if $f\left(X\right)=Y$

$f\left({f}^{-1}\left(B\right)\right)=B$, only if $B\subseteq X$

$f\left({f}^{-1}\left(B\right)\right)=B$

**Q.**Determine the point on the graph of the equations 2x+5y=20 whose x-coordinate is 52 times its ordinate.

- (2, 3)
- (2, 5)
- (5, 2)
- (5, 1)

**Q.**

Point P(2, -3) lies on the line represented by the equation:

x + 2y = 0

2x + 2y = 0

x + y = 1

2x + y = 1

**Q.**

The linear equation y= x + 2 has-

Exactly one solution

Exactly two solutions

Infinitely many solutions

No solution

**Q.**The linear equation 3x − 5y = has

(a) a unique solution

(b) two solutions

(c) infinitely many solutions

(d) no solution

**Q.**

Places A and B are 200 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 4 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars? [4 MARKS]

**Q.**

The number of solutions to the equation $\sqrt{6-4x-{x}^{2}}=x+4$ is:

$0$

$1$

$2$

$4$

**Q.**

A three-wheeler scooter charges 15rupees for first km and 8rupees for every subsequent km. For a distance of x km, an amount of y rupees is paid. Write the linear equation representing the above information

**Q.**

When 5 times the larger of the two numbers is divided by the smaller , the quotient and the remainder is 2 and 9 respectively . Form a linear equation in two variables

**Q.**The equation of the line shown in the graph is

- x+2y=0
- 2x+y=0
- 2x−y=0