Solution of a Single Linear Equation in Two Variables

Q. The equation $x+y=100$ has solution/ solutions.

1. One
2. two
3. three
4. infinitely many

Q.

Write the equations corresponding to the following statements:

Thrice a number $y$ increased by $4$ equals $11$.

Q. Find the value of k, if x = 1, y = 2 is a solution of the equation 3x + 2y = k.

1. 5
2. 3
3. 7
4. 11

Q. The sum of four times of Keerthi's age and twice the age of her brother Shankar is 64. Choose the equation(s) that represent(s) the following situation accordingly.
(Assume Keerthi's age to be '$x$' and Shankar's age to be '$y$'.)

1. $4x+2y=64$
2. $2x+y=32$
3. $2x+4y=64$
4. $x+2y=32$

Q. Which value of k gives the solution x = 10 and y = 5 for the linear equation x = 4y - 2k ?

1. 11
2. -4
3. -2
4. 5

Q.

Which of the following equations have x = 2, y = 1 as the solution?

1. 2x + 5y = 9

2. 5x + 3y = 14

3. 2x + 3y = 17

4. -x + 2y = 8

Q. The equation of x axis and a line parallel to x axis are ____ and ______ respectively.

1. y = 0 and x = a
2. x = 0 and y = a
3. y = 0 and y = a
4. x = 0 and x = a

Q. Which of the following correctly represents when b = 0 in the standard equation ax + by + c = 0

1. ax + c = 0
2. ax + by + c = 0
3. by + c = 0
4. None of the above

Q.

Identify the points which lie on the line $3x+4y=7.$

1. $(1,1)$

2. $(0,\frac{7}{4})$

3. $(0,7)$

4. $(\frac{7}{3},0)$

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

Q.

Which of following is a solution of the equation, $2x+3y=11?$

1. $x=1,y=3$

2. $x=9,y=1$

3. $x=0,y=5$

4. $x=-2,y=-5$

Q. Is $x=-3$ and $y=4$ a solution of $2y+3x+1=0$

Q.

Anil is $\mathrm{x}$ years old. Express the following in algebraic form.

What is his fathers age, if he is $15\mathrm{yr}$ more than double of Anils age?

Q.

If $29x+37y=103,37x+29y=95$ then:

1. $x=1,y=2$

2. $x=2,y=1$

3. $x=2,y=3$

4. $x=3,y=2$

Q. Find the greatest value of $c$ in order that the equation $14x+11y=c$ may have exactly five solutions in positive integers.