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. 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.

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. 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.

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