General Form of a Linear Equation in Two Variables

Q. Akhila went to a fair in her village. She wanted to enjoy rides in the Giant Wheel and play Hoopla (a game in which you throw a rig on the items kept in the stall, and if the ring covers any object completely you get it.) The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. Each ride costs Rs 3, and a game of Hoopla costs Rs 4. If she spent Rs 20 in the fair, represent this situation algebraically and graphically.

Q.

Solve

$\frac{a}{b}x-\frac{b}{a}y=a+b$

$ax-by=2ab$

Q.

X/a+y/b=2;ax-by=a^{​​​​​​2}​-b^​​​2

Q. 5 pens and 6 pencils together cost Rs 9 and 3 pens and 2 pencils cost Rs 5. Find the cost of 1 pen and 1 pencil.

Q.

Question 8
Find the solution of the linear equation x + 2y = 8 which represent a point on:
(i) x-axis
(ii) y-axis

Q.

Express the linear equation $y-2=0$ in the form $ax+by+c=0$ and indicate the values of $a,b$ and $c$.

Q.

What is alpha, beta, gamma

And how to use it in equation's

Plz tell me!

Q.

A linear equation $2x-5y=7$has

1. A unique Solution

2. Two Solutions

3. Infinite Many Solutions

4. No Solution

Q. 7 audio cassettes and 3 video cassettes cost Rs 1110, while 5 audio cassettes and 4 video cassettes cost Rs 1350. Find the cost of an audio cassette and a video cassette.

Q. 5 books and 7 pens together cost Rs 79 whereas 7 books and 5 pens together cost Rs 77. Find the total cost of 1 book and 2 pens.

Q.

The conditions for $ax+by+c=0$ to be a linear equation in two variables $(x,y)$ are

1. b can be 0 but not a

2. $a\ne 0andb\ne 0$

3. a =0 and b = 0

4. a can be zero but not b

Q. The cost of 4 pens and 4 pencil boxes is ₹100 . Three times the cost of a pen is ₹15 more than the cost of a pencil box . Form the pair of linear equations for the above situation . Find the cost of a pen and a pencil box.

Q. Question 3
Draw the graph of the linear equation 3x + 4y = 6.
At what points, the graph cuts x and y-axes?

Q. Draw graph of following pair of linear equations:
y = 2(x - 1)
4x + y = 4
Also write the coordinate of the points where these lines meets x-axis and y - axis.

Q. If $\frac{1}{x}+\frac{2}{y}=4\mathrm{and}\frac{3}{y}-\frac{1}{x}=11$ then
(a) x = 2, y = 3 (b) x = − 2, y = 3 (c) $x=-\frac{1}{2},y=3$ (d) $x=-\frac{1}{2},y=\frac{1}{3}$

Q. If 2x + 3y = 12 and 3x − 2y = 5 then
(a) x = 2, y = 3 (b) x = 2, y = − 3 (c) x = 3, y = 2 (d) x = 3, y = − 2

Q.

Express the linear equations $3x+2=0$ in the form $ax+by+c=0$ and indicate the values of $a,b$ and $c$.

Q. Question 14
The graph of the linear equation 2x + 3y = 6 is a line which meets the X-axis at the point:

A) (0, 2)
B) (2, 0)
C) (3, 0)
D) (0, 3)

Q. The cost of 2kg of apples and 1 kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2kg of grapes is Rs. 300 Represent th situation algebraically and geometrically.

Q. My friend has 4 more than twice the number of chocolates I have. If I have $x$ chocolates, then the equation representing this information is .

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

Q. Form the pair of linear equations in the following problems, and find their solution graphically:

(i) 10 students of class X took part in Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

(ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and a pen.

(iii) Champa went to a sale to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, "The number of skirts is two less than twice the number of pants purchased. Also the number of skirts is four less than four times the number of pants purchased." Help her friends to find how many pants and skirts Champa bought.

Q. { 4. Number of values(s) of }A for which the system of }}{ equations }x^2=y^2 and }(x-A)^2+y^2=1 has exactly }3} solutions, is

Q. Fathers age is three times the sum of age of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.

Q.

Which one of the following options is true, and why?

$y=3x+5$ has ,

1. A unique solution

2. Only two solutions

3. Infinitely many solutions

Q.

Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Q. Find the coordinates of the point at which the line represented by the equation 2x+3y = 8 intersects the x-axis.

Q.

If $3x=2y-2$ is written in the standard form $ax+by+c=0$, what will be the possible values of $a,b$ and $c$?

1. a = 1, b = -2 and c = 2

2. a = 3, b = -2 and c = 2

3. a = -3, b = -2 and c = 1

4. a = -3, b = 2 and c = -2

Q.

Solve by any method

x/a-y/b=a-b

x/a^2-y/b^2=0

Q. Compare the given quadratic equations to the general form and write values of a, b, c.
(1) x² – 7x + 5 = 0
(2) 2m² = 5m – 5
(3) y² = 7y

Q.

Question 2
Solve 2x + 3y = 11 and 2x - 4y = - 24 and hence find the value of 'm' for which y = mx + 3.