Linear Equation

Q.

The general form of linear equation in one variable is

1. Ax+B=C where A , B , C are rational numbers and A≠0

2. Ax+b +cz +d=0

3. (b) Ax +B =C where A , B , C are real numbers

4. Ax + B =C, where A≠0 and A , B , C are real numbers

Q. Write the linear equations in two variables for the given information :
Five years from present, the age of Sachin will be three times that of his son. Five years ago, Sachin’s age was seven times that of his son.

Q.

In a planet other than earth, the days of week in order are Sunday, Friday, Tuesday, Thursday and Monday. If two days ago, it was Friday. What is today?

1. Sunday

2. Tuesday

3. Thursday

4. Monday

Q.

The equation $3x-5y=15+3x$ has

1. 1 solution

2. 2 solution

3. no solution

4. infinite solutions

Q. Express the given information in mathematical form using two variables:
(i) Five years hence a man’s age will be three times his son’s age. The man's age is given by 'x' and his son's age by 'y'.
(ii) One number is 5 more than seven times the other number.

Q. Which of the following equations represents a line parallel to y-axis?

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

Q.

If (a, 0) is a point on the line represented by the equation $2x-3y=4,$, find the value of a.

1. 0

2. 2

3. 1

4. -1

Q.

If the equation is $h-8=5$ and the value of the variable is $h=13$ check whether it satisfies the equation or not?

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:

Q. Rs.$120$ are divided among A, B, C such that A" share is Rs.$20$ more than B"s and Rs.$20$ less than C"s. What is B"s share?

1. Rs.$10$
2. Rs.$20$
3. Rs.$30$
4. Rs.$40$

Q. Question 2
Write whether the following statement is True or False?
The graph of the linear equation x + 2y = 7 passes through the point (0, 7).

Q.

The equation $3x-5y=15+3x$ has

1. no solution

2. 2 solution

3. 1 solution

4. infinite solutions

Q.

Question 1
Points A(5, 3) B(-2, 3) and D(5, -4) are three vertices of a square ABCD. Plot these points on a graph paper and hence, find the coordinates of the vertex C.

Q. 5x+2=6 is a linear equation in one variable.

1. True
2. False

Q. The graph for the linear equation given below

Q. The average age 8 men is increased by 2 years when two of them whose ages are 21 years and 23 years are replaced by two new men . The average age of the two new men is _______________

1. 24 years
2. 28 years
3. 22 years
4. 30 years

Q.

If (a, 0) is a point on the line represented by the equation $2x-3y=4,$, find the value of a.

1. 1

2. 2

3. 0

4. -1

Q. Burst the equations that have $a=9$ on comparing with general form of a linear equation in two variables.

1. 3x+6y+8=0
2. 9y+5x+6=0
3. 9x+6y+7=0
4. 7y+9x+7=0
5. 2y+7= -9x
6. 6x+3x+4y=5
7. 5y+7x+2x+6=0
8. 9+8x+9y=0

Q.

Is -2 a solution of the linear equations $4x-2=8$ and $2x=-4$ ?

1. -2 satisfies only 4x-2=8

2. -2 satisfies only 2x = -4

3. -2 satisfies both 4x-2=8 and 2x = -4.

4. x= -2 doesn't satisfy either of the equations

Q.

$\frac{1}{x}=45$

From the above equation Value of 45x can be found as__

Q.

x = −5 can be expressed as a linear equation in 2 variables.

1. False

2. True

Q.

Complete the entries in the third column of the table.

Linear Equation	Value of Variable	Equation Satisfied (YES /NO)
$\frac{\text{x}}{\text{6}}\text{+ 5 = 10}$	$\text{x = 20}$

Q. If the point $(1,2)$ lies on the graph of the equation $2y=ax-4$. Find the value of $a$ and hence draw the graph of the linear equation.

1. $a=6$
2. $a=3$
3. $a=9$
4. $a=8$

Q. Which of the following expressions are polynomials in one variable and which are not?

$\left(i\right)4x^2-3x+7$

$\left(ii\right)y^2+\sqrt{2}$

$\left(iii\right)3\sqrt{t}+t\sqrt{2}$

$\left(iv\right)y+\frac{2}{y}$

$\left(v\right)x^{10}+y^3+t^{50}$

Q. Which of the following equations represents a line parallel to y-axis?

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

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.

If the equation is $b+5=9$ and the value of variable is $b=9$ check whether it satisfies the equation or not ?

Q.

What will you substitute to make the following equation a linear equation

$\frac{1}{x}$ + $\frac{3}{y}$ = 1

1. Either A or B

2. x as $\frac{1}{p}$ and y as $\frac{1}{q}$

3. None of the above

4. $\frac{1}{x}$ as p and $\frac{1}{y}$ as q

Q. If $9$ is the solution of variable $x$ in the equation $\frac{5x-7}{2}=y$, then the value of $y$ is $28$.

1. True
2. False

Q.

Oral Questions:

What does an equation consist of?