Linear Equations in Three Variable

Q.

Solve the following systems of the equation:

X+Y=2XY, X-Y/XY=6

Q.

Solve the pair of linear equations:

1/2x+1/3y=2

1/3x+1/2y=13/6

Q.

For what value of k, the system of equations x+y-4=0 and 2x+ky-3=0 has no solution.

Q.

Solve: $99x+101y=499,101x+99y=501$

Q. Solve for equations 5/(x+y)-2/(x-y)+1=0 and 15/(x+y)+7/(x-y)-10=0.

Q.

Solve the following pair of equations:
7x - 15y = 2 ; x + 2y = 3.
Hence find 'm' in y = mx - 30/29

1. ¹⁹/₂₉

2. 1

3. ³⁰/₂₉

4. ¹⁹/₂₉

Q. Solve by cross multiplication method ax +by = a-b bx - ay = a+b

Q. Solve:
3x - 2y + z = 2
2x + 3y - z = 5
x + y + z = 6

1. x = 1, y = 2, z = 3
2. x = 2, y = 1, z = 3
3. x = 3, y = 1, z = 2
4. x = 2, y = 3, z = 1

Q. Solve:
$2x-3y+4z=0$
$7x+2y-6z=0$
$4x+3y+z=37$

1. $x=2$
   $y=9$
   $z=15$
2. $x=4$
   $y=12$
   $z=10$
3. $x=2$
   $y=8$
   $z=5$
4. $x=5$
   $y=2$
   $z=8$

Q. A number cosists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits be reversed. Find the number.

1. 325
2. 253
3. 523
4. 311

Q.

Find the solution to the following system of linear equations:
2x+3y=8
x-2y+3=0

1. (-1, 2)

2. (1, 3)

3. (3, 1)

4. (1, 2)

Q. Solve the following system of linear equations in three variables.
2x - 7y + 11z = 0
6x - 8y + 7z = 0
3x + 4y + 5z = 35

1. x = 1, y = 2, z = 3
2. x = 0, y = 4, z = 1
3. x = 3, y = 4, z = 2
4. x = - 1, y = 2, z = 1

Q.

Form a Quadratic polynomial whose sum of zeros is $4$ and the product of zeros is $8$.

Q.

Sheela went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received.

Q.

Construct two equations having solution $\text{x = -2}$

Q.

${\text{Find the product of all the zeroes of the cubic polynomial 3x}}^3-5x^2+8x-12.$

Q.

If the zeroes of the polynomial ${\mathrm{x}}^3-3{\mathrm{x}}^2+\mathrm{x}+1$ are$\mathrm{a}-\mathrm{b}$, $\mathrm{a}$, $\mathrm{a}+\mathrm{b}$, find $\mathrm{a}$ and $\mathrm{b}$.

Q.

Express the linear equations in the form $ax+by+c=0$ and indicate the values of $a,b$ and $c$ in each case $2x=-5y$.

Q.

Question 1 (ii)
Form the pair of linear equations in the following problems, and find their solutions graphically.
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 that of one pen.

Q. Solve the following equations:
$2x-3y+5z=11$
$5x+2y-7z=-12$
$-4x+3y+z=5$

1. $x=10,y=1,z=9$
2. $x=2,y=1,z=3$
3. $x=10,y=6,z=3$
4. $x=1,y=2,z=3$

Q.

Solve the equation

1÷2x-1÷y=-1

1x+1÷2y=8

Q. There is a certain number consisting of 3 digits which is equal to 25 times the sum of the digits, and if 198 be added to the number, the digits will reversed, also the sum of the extreme digits exceeds the middle digit by unity. Find the number

1. 753
2. 345
3. 375
4. 573

Q. Solve the following system of equations 8x+7y=2xy 6x+y=10xy (x is not equal to 0, y is not equal to 0)

Q. $\alpha ,\beta$ & $\gamma$ are the zeroes of cubic polynomial $P\left(x\right)=a{x}^3+b{x}^2+cx+d,(a\ne 0)$ then product of their zeroes $[\alpha .\beta .\gamma ]=$ .................

1. $\frac{-b}{a}$
2. $\frac{a}{b}$
3. $\frac{-d}{a}$
4. $\frac{c}{a}$

Q. Solve the linear equations by elimination method 2x/3+3y/4=1/12; 3x/4-2y/3=-1/2

Q. Solve the following system of linear equation in three variables.
5x + 6y + 8z = 0
3x + 4y + 6z = 0
3x + 5y + 16z = 7

1. x=2 , y= 4 and z=1
2. x=2 , y= -3 and z=2
3. x=2 , y= -3 and z=1
4. x=3 , y= -3 and z=1

Q. Solve for x and y
ax\b - by\a is equal to a plus b
As - by is equal to 2ab
Is it quadratic equations or linear equations chapter??😅😅

Q. Question 10
A pair of linear equations which has a unique solution x = 2 and y = - 3 is
(A) x + y = 1 and 2x – 3y = -5
(B) 2x + 5y = - 11 and 4x + 10y = - 22
(C) 2x – y = 1 and 3x + 2y = 0
(D) x – 4y + 14 = 0 and 5x – y – 13 = 0

Q.

Write the equation y = 3x + 2 in the form ax + by + c = 0, and indicate the value of a b and c

Q. Solve the following system of linear equations in three variables.
$x+y+z=52x-y+z=9x-2y+3z=16$

1. $x=18y=\frac{-19}{3}z=-4$
2. $x=-4y=18z=-\frac{19}{3}$
3. $x=2y=-1z=4$
4. $x=-\frac{19}{3}y=18z=-4$