Linear Equation in Two Variables

Q.

It is known that $x+y=10$ and that $x=z$. Show that $z+y=10$ ? Solve the following question using appropriate Euclid’s axiom.

Q.

If xyz=1 , then show that (1+x+y^{​​​​​​-1})^-1 + (1+y+z^{​​​​​​-1})^-1 + (1+z+x^{​​​​​​-1})^-1 =1

Q.

F=(9/5)C+32

Is there a temperature which is numerically the same in both Fahrenheit and celcius? If yes, find it.

Explain the solution with reason.

Q. Draw the graph of 3x + 5y = 15

Q. The graph of x = 3 is a line:

1. Parallel to the x-axis at a distance of 3 units from the origin
2. Makes an intercept 3 on the y-axis
3. Parallel to the y-axis at a distance of 3 units from the origin
4. Makes an intercept 3 on the x-axis

Q. The equation x = 0 represents ___ axis.

Q.

If x + y + z = 0, then the value of x³ + y³ + z³ is

1. 3 xyz

2. 6 xyz

3. 9 xyz

4. 24 xyz

Q.

Solve the following simultaneous liner equations by subsitution method

mx-ny=m²+n²

x+y=2m

Q.

The graph of every linear equation in two variables is --------------.

1. Straight line

2. Hyperbola

3. Parabola

4. Curve

Q. Only 60% and 50% of eligible voters of town A and B respectively, cast their vote in the election. The total number of votes cast were $1200.$
Which of the following linear equations represents this scenario accurately?
(Assume number of eligible voters in town A to be $x$ and in town B to be $y$)

1. $5x+6y=12000$
2. $6x+5y=12000$
3. $5x+6y=1200$
4. $6x+5y=1200$

Q.

if x +y+ 4 =0 , then find the value of x³ + b³ - 12xy + 64

Q.

The highest power of the variable in a linear equation is _____.

Q.

Prove that:

x² + y² + z² - xy - yz - zx is always positive.

Q.

The graph of a linear equation is

1. a curve

2. a straight line

3. a zig-zag line

4. None of these

Q.

if m = a^x , n=a^y and a² = (m^yn^x)^z then xyz =

Q. Express the following statement as a linear equation in two variables.
The sum of a two-digit number and the number obtained by reversing the order of its digits is 55.
Assume the digits in ones and tens place are ‘x’ and ‘y’ respectively.

1. x + y = 5
2. 55x + 55y = 11
3. 5x + 5y = 11
4. 11x + 11y = 5

Q.

Find the value of x & y, when 25^x=5^y-1& (32)^y=4x8^x

1. 

2. 

3. 

4. 

Q.

List the methods used in solving linear equations.

Q.

The sum of two numbers is $12$

Their difference is $4$.

How do you find the numbers?

Q. Represent $3x+5y=15$ on a graph.

Q. Question 7
Write whether the following statement is True or False?
The graph of every linear equation in two variables need not be a line.

Q. The graph of the linear equation 2x - y = 4 cuts x-axis at

Q.

A rabbit covers y metres distance by walking 10 metres in slow motion and the remaining by x jumps , each jump contains 2 metres.

Express the information in linear equation.

Q. The graphical representation of a linear equation in two variables is a ___.

1. curve
2. circle
3. parabola
4. straight line

Q.

If 13x - 2y + 34 = 19 - 2y is represented in the form of ax + by + c = 0, then what is the value of b?

1. 0

2. 4

3. -4

4. 2

Q.

The geometrical representation of a linear equation is a:

1. Straight line

2. parabola

3. circle

4. curve

Q. Which one of the following equations is an example of a linear equation in two variables?

1. $xy+2y=2$
2. $x+2y+3z=4$
3. $7x=5$
4. $3x-6y=8$

Q. I have a certain number of chocolates. My friend has 4 more than twice the number of chocolates I have. Which of the following equations depicts the relation between the number of chocolates with me and my friend?
(Assume $x$ as number of chocolates I have and $y$ as number of chocolates my friend has.)

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

Q.

The linear equation $2x-5y=7$ has,

1. A unique solution

2. Two solutions

3. Infinitely many solutions

4. No solution

Q. Animesh bought 10 pencils and 7 erasers and the total amount he paid was rupees 120. Choose the equation that represents the transaction correctly.
(Assume the price of a pencil to be ₹ $x$ and of an eraser to be ₹ $y$)

1. $10x+7y=120$
2. $10x-7y=120$
3. $5x+3y=40$
4. $7x+10y=120$