Solution of Linear Equation in 2 Variables

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

1. $(\frac{-49}{29},\frac{14}{39})$
2. $(3,\frac{-19}{29})$
3. $(\frac{-13}{29},\frac{14}{29})$
4. $(\frac{49}{29},\frac{19}{29})$

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)

1. $24000$

2. $25500$

3. $26000$

4. $24500$

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. 1

2. 2

3. 4

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:

$$\begin{gathered} 8x+5y=9 \\ 3x+2y=4 \end{gathered}$$

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 =

1. 5

2. 6

3. 3

4. 4

Q.

$Ifx=1andy=6\text{is a solution of the equation}8x-ay+a^2=0,\text{find the values of a.}$

Q. Question 4
The linear equation that converts Fahrenheit (F) to Celsius (C) if is given by the relation, $C=\frac{5F-160}{9}$

(i) If the temperature is ${86}^{\circ }$F, what is the temperature in Celsius?

(ii) If the temperature is ${35}^{\circ }$C, what is the temperature in Fahrenheit?

(iii) If the temperature is $0^{\circ }$C, what is the temperature in Fahrenheit and if the temperature is $0^{\circ }$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.

1. Man = 50 years Son = 25 years
2. Man = 60 years Son = 20 years
3. Man = 50 years Son = 20 years
4. Man = 50 years Son = 10 years

Q.

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

1. 3

2. 1

3. 2

4. 4

Q.

Write two solutions for each of the following equations:

(i) $3x+4y=7$ (ii) $x=6y$ (iii) $x+\pi y=4$ (iv) $\frac{2}{3}x-y=4$

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

1. 13
2. 75
3. 65
4. 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) $(\sqrt{3},0)$ (v) $(\frac{1}{2},-5)$

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?

1. Infinitely many

2. Two

3. Only one

4. 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. $1$

2. $2$

3. $3$

4. $4$

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

1. $7y^2$

2. $8y$

3. $7$

4. $14y$

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

1. 2x-3y=5

2. 2x+3y=4

3. 4x-2y=6

4. 2x-4y=-4

Q.

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