Elimination Method of Finding Solution of a Pair of Linear Equations

Q. If $3x–4y=1$ and $5x–6y=7,$ then $x+y$ = ___.

1. 16
2. 19
3. 20
4. 18

Q.

Solve for x and y:

$\frac{3}{x+y}+\frac{2}{x-y}=2,\frac{9}{x+y}-\frac{4}{x-y}=1.$
[Concept name: Elimination Method]
(3 Marks)

Q. The cost of a room in a hotel is partially fixed and partially varying with reapect to the number of hours. A person staying for 10 hours paid ₹600 and a person staying for 15 hours paid ₹840. Find the fixed cost and the variable cost per hour.

1. ₹120, ₹48/hr
2. ₹120, ₹100/hr
3. ₹200, ₹48/hr
4. ₹200, ₹120/hr

Q.

Select the correct approach for solving a pair of linear equations in 2 variables by elimination method.
i) Add or subtract one equation from the other so that one variable gets eliminated.
ii) Multiply both the equations by any non-zero constant to make the coefficients of one variable (either x or y) numerically equal.
iii) Solve the equation in one variable (x or y) to get its value.
iv) Substitute the value of x (or y) in either of the original equations to get the value of the other variable.

1. (i), (iv), (ii), (iii)

2. (ii), (i), (iv), (iii)

3. (ii), (i), (iii), (iv)

4. (i), (ii), (iii), (iv)

Q. The sum of two numbers is 8. If their sum is four times their difference, find the numbers.

1. 5, 3
2. 7, 4
3. 9, 6
4. 10, 7

Q.

Select the correct order for solving a pair of linear equations in two variables by elimination method.

i) Add or subtract one equation from the other so that one variable gets eliminated.

ii) Multiply both the equations by any non-zero constant to make the coefficients of any one of the variables numerically equal.

iii) Substitute the obtained value in either of the original equations to get the value of the other variable.

iv) Solve the equation in one variable thus obtained to get its value.

1. (i), (iv), (ii), (iii)

2. (ii), (i), (iii), (iv)

3. (i), (iv), (iii), (ii)

4. (ii), (i), (iv), (iii)

Q.

Find the solution of the following pair of equations.
$3x-5y=-1$ and $x-y=-1$

1. x = - 2 and y = - 1

2. x = 3 and y = - 1

3. x = - 1 and y = - 2

4. x = - 1 and y = - 4

Q.

Solve the following pair of equations:
$2x+y=7$
$3x+2y=12$
Choose the correct answer from the given options.

1. (1, 0)

2. (-3, 2)

3. (2, 3)

4. (3, 2)

Q.

For the given pair of linear equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0,$ the solution $(x,y)$ is

1. ((b₂c₂-b₁c₁)/(a₁b₂-a₂b₁), (c₂a₂-c₁a₁)/(a₁b₂-a₂b₁))

2. None of these

3. ((b₂c₁-b₁c₂)/(a₁b₂-a₂b₁), (c₁a₁-c₂a₂)/(a₁b₂-a₂b₁))

4. ((b₁c₂-b₂c₁)/(a₁b₂-a₂b₁), (c₁a₂-c₂a₁)/(a₁b₂-a₂b₁))

Q. In a two-digit number, the units digit is twice the tens digit. If 27 is added to the number, the digits interchange their places. Find the number.

1. 63
2. 36
3. 69
4. 96