Solving SImultaneous Linear Equations by Elimination Method

Q.

Solve the following equation:$\frac{7y+4}{y+2}=\frac{-4}{3}$

Q. Solve:
$2x-9y=9,5x+2y=27$

1. $x=\frac{261}{49},y=\frac{9}{49}$
2. $x=\frac{9}{49},y=\frac{261}{49}$
3. $x=\frac{19}{49},y=\frac{26}{49}$
4. $x=\frac{49}{261},y=\frac{49}{149}$

Q.

X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by 1.5 hours. The speed of X is:

1. $\frac{9}{7}km/hr$

2. $\frac{10}{3}km/hr$

3. $5km/hr$

4. $9km/hr$

Q. 4 chairs and 3 tables cost ₹ 2100 and 5 chairs and 2 tables cost ₹ 1750. Find the cost of a chair.

1. ₹ 130
2. ₹ 100
3. ₹ 200
4. ₹ 150

Q.

X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by $1\frac{1}{2}$ hours. The speed of X is:

1. $\frac{10}{3}km/hr$

2. $9km/hr$

3. $\frac{9}{7}km/hr$

4. $5km/hr$

Q. Rohit can row downstream 32 km in 4 hours and upstream 4km in 1 hour. Find his speed of rowing in still water and speed of the current.

1. 20 km/hr, 4 km/hr
2. 4 km/hr, 2 km/hr
3. 6 km/hr, 2 km/hr
4. 4 km/hr, 4 km/hr

Q.

Solve the following pairs of equations:
$\frac{1}{x}+\frac{3}{y}=1$
$\frac{6}{x}-\frac{12}{y}=2$
(Where $x\ne 0,y\ne 0)$

1. $x=\frac{5}{3},y=\frac{15}{2}$

2. $x=\frac{3}{5},y=\frac{7}{3}$
   

3. $x=3,y=11$

4. $x=4,y=9$

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

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

Q. Solve the following pair of linear equations:
$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$
$\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$
(Where $x>0,y>0)$

1. $x=4,y=9$
2. $x=9,y=4$
3. $x=3,y=2$
4. $x=\frac{1}{2},y=\frac{1}{3}$

Q.

54 is divided into two parts such that sum of 10 times the first part and 22 times the second part is 780. What is the bigger part?

1. 34

2. 32

3. 30

4. 24

Q.

Find the value of x?

x + y = 5
3x - y = 3

1. -3

2. -2

3. 2

4. 3