Solving Simultaneous Linear Equations by Substitution Method

Q. What is the solution for the following pair of linear equations?

$\frac{1}{2x}-\frac{1}{y}=-1$

$\frac{1}{x}+\frac{1}{2y}=8$

(where $x\ne 0,y\ne 0)$

1. $x=\frac{1}{7},y=\frac{1}{2}$
2. $x=\frac{1}{8},y=\frac{1}{3}$
3. $x=\frac{1}{6},y=\frac{1}{4}$
4. $x=\frac{3}{4},y=\frac{5}{4}$

Q. The value of a for which the lines $x=1$, $y=x$ and $a^{2}x+2ay-24=0$ are concurrent is:

1. a = 4 or a = -6
2. a = 4 or a = -4
3. a = -4 or a = 6
4. a = 6 or a = -6

Q.

Find two numbers whose sum is $-18$‘ and the difference is ’$-4$.

Q. The ratio of incomes of two persons is $9:7$. The ratio of their expenses is $4:3$. Every person saves ₹ 200 , find the income of each.

Q.

For the equation y = 3x - 7, if y = 0, then what is the value of x?

1. -7/3

2. 0

3. 7/3

4. 7

Q. How will you make the following equations linear?
$\frac{5}{x-1}+\frac{1}{y-2}=2$
$\frac{6}{x-1}+\frac{3}{y-2}=1$
(Where $x\ne 1,y\ne 2)$

1. Substitute $\frac{1}{x-1}$ as p and $\frac{1}{y-2}$ as q
2. Subsitute $\frac{1}{x-1}$ as $\frac{1}{p}and\frac{1}{y-2}$ as $\frac{1}{q}$
3. Substitute $x=X+1$ and $y=Y+2$
4. The equation is already linear