Solving Simultaneous Linear Equations by Cross Multiplication Method

Q. The sum of two digit number and the number formed by interchanging the digits is 132. If 12 is added to the number, the new number becomes 5 times the sum of the digits. Find the number.

1. 132
2. 48
3. 39
4. 88

Q. 2x – 4y = 7
x – 3y = –2
The given set of equations has______.

1. Unique solution
2. Many solutions
3. None of these
4. No solution

Q. A fraction becomes $\frac{4}{5}$ if one is added to both numerator and denominator. If, however, 5 is subtracted from numerator and denominator, the resultant fraction becomes $\frac{1}{2}$. Find the fraction.

1. $\frac{-7}{9}$
2. $\frac{7}{10}$
3. $\frac{-7}{10}$
4. $\frac{7}{9}$

Q. Assertion: y = mx represents a line passing through the origin.
Reason: Any line parallel to the x-axis is y = k.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Q. If the number obtained by interchanging the digits of a two digit number is 18 more than the original number and the sum of the digits is 8, then find the original number.

1. 25
2. 35
3. 40
4. 30

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. $x=4,y=9$

2. $x=3,y=11$

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

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

Q.

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

1. $x=4,y=9$
2. $x=\frac{3}{5},y=\frac{7}{3}$
3. $x=\frac{5}{3},y=\frac{15}{2}$
4. $x=3,y=11$