# Solution of Linear Equation in 2 Variables

## Trending Questions

**Q.**The point of intersection of lines 3x+6y=9 and 7x–15y=2 is

- (−4929, 1439)
- (3, −1929)
- (−1329, 1429)
- (4929, 1929)

**Q.**

Question 5

The graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point:

A) (2, 0)

B) (0, 3)

C) (3, 0)

D) (0, 2)

**Q.**

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Aarushi paid Rs 27 for a book kept for seven days. If fixed charges are Rs x and per day charges are Rs y, write the linear equation representing the above information.

**Q.**

Swati starts her job with certain monthly salary and earns a fixed increment every year. If her salary was Rs 22500 per month after 6 years of service and Rs 30000 per month after 11 years of service. Find her salary after 8 years of service (in Rs)

$24000$

$25500$

$26000$

$24500$

**Q.**

The ratio of incomes of two persons A and B is $3:4$ and the ratio of their expenditures is $5:7$. If their savings are $\text{Rs}.15,000$ annually find their annual incomes. What value will be promoted if the expenditure is under control?

**Q.**

If (2k - 1, k) is a solution of the equation 10x - 9y = 12, then k =

1

2

4

3

**Q.**

If x=1, y=2 is a solution of equation a^2 x +ay =3, then find the value of a

**Q.**

Solve the following pair of linear equations by the substitution methods:

$8x+5y=9\phantom{\rule{0ex}{0ex}}3x+2y=4$

**Q.**

A number is 27 more than the number obtained by reversing its digits. If its unit's and ten's digit are x and y respectively, write the linear equation representing the above statement.

**Q.**

Express y in the term of x given that 2 x - 5 y = 7 check weather the (-3, -2) lies on the graph of the given linear equation

**Q.**Question 3 (iii)

Form the pair of linear equations for the following problems and find their solution by substitution method:

The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.

**Q.**

Write four solutions for the given equation:

$3x+4y=7$

**Q.**

If (4, 19) is a solution of the equation y=ax+3, then a =

5

6

3

4

**Q.**

If x=1 and y=6 is a solution of the equation 8x−ay+a2=0, find the values of a.

**Q.**Question 4

The linear equation that converts Fahrenheit (F) to Celsius (C) if is given by the relation, C=5F−1609

(i) If the temperature is 86∘F, what is the temperature in Celsius?

(ii) If the temperature is 35∘C, what is the temperature in Fahrenheit?

(iii) If the temperature is 0∘C, what is the temperature in Fahrenheit and if the temperature is 0∘F, what is the temperature in Celsius?

(iv) What is the numerical value of the temperature which is same on both the scales?

**Q.**

Plot the points (3, 5) ad (-1, 3) on a graph paper and verify that the straight line passing through these points also passes through the point (1, 4).

**Q.**Ten years hence, a man's age will be twice the age of his son. Ten years ago, the man was four times as old as his son. Find their present ages.

- Man = 50 years Son = 25 years
- Man = 60 years Son = 20 years
- Man = 50 years Son = 20 years
- Man = 50 years Son = 10 years

**Q.**

If (a, 4) lies on the graph of 3x + y = 10, then the value of a is

3

1

2

4

**Q.**

Write two solutions for each of the following equations:

(i) 3x+4y=7 (ii) x=6y (iii) x+πy=4 (iv) 23x−y=4

**Q.**Sum of two integers is 88. If the greater integer is divided by the smaller integer, the quotient is 5 and the remainder is 10, then the greater integer is

- 13
- 75
- 65
- 23

**Q.**

Check which of the following are solutions of the equation 2x−y=6 and which are not: (i) (3, 0) (ii) (0, 6) (iii) (2, −2) (iv) (√3, 0) (v) (12, −5)

**Q.**

5x-3y=1

2x+5y-19=0

**Q.**

Give the equations of two lines passing through $(2,14)$. How many more such lines are there, and why?

**Q.**

How many linear equations are satisfied by x = 2 and y = -3?

Infinitely many

Two

Only one

Three

**Q.**

If $x\%$ of $y$ is equal to $1\%$ of $z$, $y\%$ of $z$ is equal to $1\%$ of $x$ and $z\%$ of $x$ is equal to $1\%$ of $y$, then the value of $xy+yz+zx$ is.

$1$

$2$

$3$

$4$

**Q.**

Question 10

Let y varies directly as x. if y = 12 when x = 4, then write a linear equation. What is the value of y when x = 5?

**Q.**

The number of days in $y$weeks and $y$ days is

$7{y}^{2}$

$8y$

$7$

$14y$

**Q.**

How do you find the solution of the system of equations $3x+4y=10$ and $x-y=1$?

**Q.**

The point(-4, -1) lies on a line of the equation

2x-3y=5

2x+3y=4

4x-2y=6

2x-4y=-4

**Q.**

Find the X intercept of 3x - 4y = 12