Equations with Two Variables

Q. A plane left 30 minutes later than the scheduled time. In order to reach the destination 1500 km away in time, it has to increase the speed by 250 km/hr from the usual speed. Find its usual speed.

1. 1000 km/hr
2. 800 km/hr
3. 680 km/hr
4. 750 km/hr

Q.

What are the three types of systems of linear equations?

Q. By using variables x and y form any five linear equations in two variables.

Q.

A linear equation in two variables has only 1 solution.

1. True

2. False

Q.

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be $₹x$ and that of a pen to be $₹y$)

Q.

$x=2$, $y=-1$is a solution of the linear equation:

1. $x+2y=0$

2. $x+2y=4$

3. $2x+y=0$

4. $2x+y=2$

Q.

A plane left 30 minutes later than its scheduled time. In order to reach the destination which is 1500 km away on time, it has to increase its speed by 250 km/hr. Find its original speed.

1. 1000 km/hr

2. 750 km/hr

3. 800 km/hr

4. 680 km/hr

Q.

If x =3, y = 2 is a solution of a linear equation in two variables, we write the solution as (3, 2). What is this notation called?

__

Q.

S1 : The graph of a linear equation is a straight line

S2 : The solution of a pair of linear equations is a point common to two lines.

1. S1 is false but S2 is true

2. S1 and S2 are true

3. S1 and S2 are false

4. S1 is true but S2 is false

Q.

On the basis of graph, the pair of linear equation gives _______________solution(s).

1. Only one

2. Infinite

3. Four

4. Zero

Q.

Question 1(e)

Fill in the blanks:
1 million = _______________ lakh.

Q.

Solve the following pair of equations.

$\frac{5}{x-1}+\frac{1}{y-2}=2$

$\frac{6}{x-1}-\frac{3}{y-2}=1$

Here, x $\ne$ 1 and y $\ne$ 2

1. x = 4, y = 5

2. x = 5, y = 3

3. $x=\frac{1}{3},y=\frac{1}{3}$

4. x = 7, y = 11

Q. How many linear equations are satisfied by x = 2 and y = −3?

(a) Only one

(b) Two

(c) Three

(d) Infinitely many

Q. Draw the graph of the equation y=3x. Does the point (3, 1) lie on this line?

Q.

Based on the graph, the pair of linear equations has _______________solution(s).

1. Only one

2. Infinite

3. Four

4. Zero

Q.

Given graph gives the solution of the linear equation

1. x=y

2. x-2=y

3. 3x+2=y

4. 4x+5=2

Q.

$20°C$ less than the present temperature. Give the corresponding Expression.

Q. Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units.

Q. Draw the graph of linear equations y = x and y = -x. What do you observe?

Q. In the equation $2x+3y=6$ , if $x=3$, then the value of $y$ is ____.

1. 0
2. 2
3. 1
4. 3

Q.

So, 2.4s + 3t = 7 is a linear equation in two variable.
A linear equation in one variable is an equation of the form ...........

1. ax + b = 0, where a, b , c are real numbers

2. ax = c, where a and c are real numbers

3. by = c, where band c are real number

4. All of above

Q.

Which of the following are Pair of Linear Equation in two variables?

1. x + 2 = 0; a + 2b = 0

2. x + y - 3 = 0; 4a + 2b + c = 24

3. 2x + y = 2; 3x - z=2

4. 12x + 4y + 3 = 0; 4x + 4y + 4 = 0

Q. Choose the option which describes the equation of the line shown in the graph.

1. x + y = 0
2. y = 2x
3. y = 2x + 4
4. y = x + 4

Q. 6x+2x=7 is a linear equation with two variables.

1. True
2. False

Q. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement

1. x = 2 y
2. x - 2y = 0
3. 2y - x = 0
4. 3y = 2 x

Q.

Plz explain me the process of sloving simultaneous equations with help of cross multiplication

Q. The value of k if (2, 3) lies on 2x=3y-k

1. 0
2. 5
3. 1
4. 4

Q. The point (3, 15) passes through the line represented by the equation .

1. $y=5x$
2. $y=4x$
3. $y=6x$

Q.

Find the solution to the following system of linear equations:

2x-y+6=0

4x+5y-16=0

1. (1, 4)

2. (-1, 4)

3. (2, 3)

4. (2, -3)

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

(iv) $3x=-7y$