Solution of a Linear Equation in Two Variables

Q. Question 2
Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:
$\left(i\right)2x+3y=9.35\left(ii\right)x-\frac{y}{5}-10=0\left(iii\right)-2x+3y=6\left(iv\right)x=3y$
$\left(v\right)2x=-5y\left(vi\right)3x+2=0\left(vii\right)y-2=0\left(viii\right)5=2x$

Q. If x – y = 4 and 2x + y = 14, then the value of x + 4y is

1. 12
2. 10
3. 14
4. 16

Q. If ad is not equal to bc, then find whether the pair of linear equation ax+by =p and cx+dy=q has no solution, unique solution or infinitely many solutions.

Q.

$x-y=0$ is a line which is

1. parallel to x-axis

2. parallel to y-axis

3. passing through (1, -1)

4. passing through origin

Q.

How many solutions of the equation 15x - 14y + 11 = 0 are possible?

1. No Solution

2. 2

3. Infinite

4. 1

Q.

The equation of a straight line passing through $(-3,2)$ and cutting an intercept equal in magnitude but opposite in signs from axes is given by:

1. $x-y+5=0$

2. $x+y-5=0$

3. $x-y-5=0$

4. $x+y+5=0$

Q.

The sum of the radii of two circles is $140cm$ and the difference of the circumferences is $88cm$. Find the diameters of the circles.

Q.

For which value of p does the pair of equation given below has unique solution?

4x + py + 8 = 0

2x + 2y + 2 = 0

Q.

The equation of the line whose slope is $3$ and which cuts off an intercept $3$ from the positive $x$ axis is

1. $y=3x–9$

2. $y=3x+3$

3. $y=3x+9$

4. None of these

Q. The pair of equation y=0 and y= -5 has _____ solution

Q. For what values of p, the linear equation 3x+py=9 has equal values of x and y for its solution

Q. If two lines intersect each other at a point, then they have

1. No solution
2. A unique solution
3. Two solutions
4. Infinite solutions

Q. find 3 solutions of the equation 2x+3y=6

Q.

Pair of linear equations x + 2y + 5 = 0 and 3x + 6y -1 = 0 have

1. No solution

2. Infinitely many solutions

3. Unique solution

4. Exactly two solutions

Q.

How do you solve a linear word problem?

Q.

A shopkeeper sells a table at $8\%$ a profit and a chair at a $10\%$ discount, thereby getting$₹1008$. If he had sold the table at $10\%$ profit and the chair at $8\%$ discount, he would have got $₹20$ more. Find the cost price of the table and the list price of the chair.

Q.

Which of the following equations have x = 7, y = 3 as solution?

1. x + 3y = 16

2. x - y + 4 = 0

3. x + y = 4

4. x + y = 7

Q. The pair of equations $2x-5y+4=0\mathrm{and}2\mathrm{x}+\mathrm{y}-8=0$ has

(a) a unique solution
(b) exactly two solutions
(c) infinitely many solutions
(d) no solutions

Q. $3x+4y=6\&6x+8y=12$ are ______.

1. intersecting lines
2. parallel lines
3. coincident lines
4. dependent pair of linear equations

Q.

Equation of the line passing through the mid-point of intercepts made by the circle $x^2+y^2-17x-16y+60=0$ is

1. $16x-17y=136$

2. $17x-16y=136$

3. $16x+17y=136$

4. $17x+16y=136$

Q. The equation $y=mx$ represents ___ ;
where, $(m\ne 0)$.

1. a line parallel to x-axis
2. a line parallel to y-axis
3. a line passing through the origin
4. a line cutting x-axis at the point $(m,0)$

Q. The pair of linear equations 4x − 5y −20 = 0 and 3x + 5y − 15 = 0 has
(a) a unique solution
(b) two solutions
(c) many solutions
(d) no solution

Q. If (x + 2y – 1) (x + 3y – 3) = 1271, where x and y are the natural numbers and (x + 2y  –  1), (x  +  3y  –  3) are prime numbers, then the value of $\frac{y}{x}$ is equal to

1. $\frac{9}{10}$
2. $\frac{3}{2}$
3. $\frac{2}{3}$
4. 1

Q.

If (2, 2) lies on $4x+5y=k$, the value of $k$ is

___

Q.

Which of these following equations have $x=-3,y=2$ as solutions?

1. 2x+3y= 0

2. 3x+2y=0

3. 2x-3y=0

4. 3x-2y=0

Q.

Check which of the following are solutions of the equation $x-2y=4$

1. $(0,2)$

2. $(2,0)$

3. $(4,0)$

4. $(\sqrt{2},4\sqrt{2})$

Q.

______ satisfies the equation $3x+4y=2$.

1. (2, 1)

2. (-2, 1)

3. (2, -1)

4. (2, 2)

Q.

Which of the following equations does not pass through point (3, 3)

1. 3x+y = 12

2. 4x-2y-6=0

3. x-y=0

4. 2x-y=6

Q.

x = 7, y = 3 is a solution for which of the following?

1. x + y = 4

2. x + 3y = 16

3. x - y + 4 = 0

4. x + y = 7

Q. $8x+5y=9$
$3x+2y=4$

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