Substitution Method

Q.

The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle. [4 MARKS]

Q. If the length of a rectangle is decreased by 3 units, and its breadth increased by 5 units, then the area of the rectangle is increased by 10 square units. If the length is increased by 3 units, and breadth decreased by 3 units, then the area is decreased by 18 square units. What is the breadth of the rectangle?

1. 3 units
2. 8 units
3. 5 units
4. 6 units

Q. Solve for 'x' and 'y', using the method of substitution:
4x + 3y = 12; x - 6y = 9

1. $x=\frac{9}{33},y=-\frac{9}{33}$
2. $x=-\frac{33}{9},y=\frac{8}{9}$
3. $x=-\frac{8}{9},y=\frac{33}{9}$
4. $x=\frac{33}{9},y=-\frac{8}{9}$

Q. If the numerator is decreased by 1 and denominator is multiplied by 2, then the resulting fraction is $\frac{1}{5}$.If the numerator is increased by 12 and denominator is multiplied by 6, then the resulting fraction is $\frac{1}{2}$. What is the difference between the numerator and the denominator?

1. -2
2. 3
3. 1
4. -5

Q.

$3X+2Y=5$

$2X-3Y=7$

Solve Them Graphically

Q. If the line represented by the equation $3x+4y+c=0$ passes through the origin, then the value of $c$ is equal to:

1. \N

Q. Solve for 'x' and 'y', using the method of substitution:
4x + 3y = 12; x - 6y = 9 [3 Marks]

Q. Solve :
$2x-3y=2,x+2y=8$
using the method of substitution.

1. $x=6,y=2$
2. $x=2,y=4$
3. $x=-4,y=-2$
4. $x=4,y=2$

Q. Solve the following pair of equations:

$7x-8y=-12$

$-4x+2y=3$

1. $x=6,y=\frac{1}{2}$
2. $x=0,y=\frac{3}{2}$
3. $x=0,y=0$
4. $x=\frac{5}{2},y=4$

Q. $\text{Given that}y=\frac{(cx+d)}{b}$;

$\text{where}b\ne 0\&(a+c)\ne 0$,

$\text{then, what is the value of}x,\text{if}ax+by+c=0?$

1. $\frac{(-d-c)}{(a+c)}$
2. $\frac{(d+c)}{(a+c)}$
3. $\frac{(a+c)}{(d+c)}$
4. None

Q. A number which when multiplied by 12 gives a result as 60, when added to 324 gives y. What s the value of y ?

1. 329

Q. Given that,
$y=\frac{(cx+d)}{b}$; where, $b\ne 0\&(a+c)\ne 0$,

then, what is the value of x, if $ax+by+c=0?$

1. $\frac{(d+c)}{(a+c)}$
2. $\frac{(-d-c)}{(a+c)}$
3. None
4. $\frac{(a+c)}{(d+c)}$

Q.

What will you substitute to make the following equation a linear equation

$\frac{1}{x}$ + $\frac{3}{y}$ = 1

1. x as $\frac{1}{p}$ and y as $\frac{1}{q}$

2. $\frac{1}{x}$ as p and $\frac{1}{y}$ as q

3. Either A or B

4. None of the above

Q. In the equation
$ax+by+c=0$,
$\text{if}y=\frac{(cx+d)}{b}$
and a = d,
then what is the value of $x$ ?

1. -1
2. -2
3. $\frac{(d+c)}{(a+c)}$
4. $\frac{(-d-c)}{(a+c)}$

Q.

For the given equations $x+y=2$ and $x-y=3$ find the value of $x$ and $y$.

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

Q. If $5x-10y=20$ and $10x+20y=40$ then find the value of $x$ by using the substitution method.
$\left[2\right]$
[2 Marks]

Q. If the numerator and the denominator of a fraction is decreased by 2, then the resulting fraction is $\frac{1}{2}$. If in case the numerator is increased by 2 and the denominator by 1, then the result is 1. The sum of the numerator and the denominator is ___.

1. 7
2. 3
3. 4
4. -7

Q.

Given that $y=\frac{(cx+d)}{b}$;

where $b\ne 0\&(a+c)\ne 0$,

then, what is the value of x, if $ax+by+c=0$?

1. $\frac{(-d-c)}{(a+c)}$

2. $\frac{(a+c)}{(d+c)}$

3. $\frac{(d+c)}{(a+c)}$

4. None

Q.

In the equation $ax+by+c=0$, if y= $\frac{(cx+d)}{b}$ and a = d, then what is the value of '$x$' ?

1. -1

2. -2

3. $\frac{(d+c)}{(a+c)}$

4. $\frac{(-d+c)}{(a+c)}$

Q. If the numerator is decreased by 1 and denominator is multiplied by 2, then the resulting fraction is $\frac{1}{5}$.If the numerator is increased by 12 and denominator is multiplied by 6, then the resulting fraction is $\frac{1}{2}$. What is the difference between the numerator and the denominator?

1. 1
2. -2
3. 3
4. -5

Q. Solve the following simultaneous equations
$0.5x+0.6y=2.3$
$0.2x+0.7y=2.3$

Q. At an event, a total participation fee of $900 was collected from participants
The equation representing the number of participants at career's talk is

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

Q.

Measure of one of the angles of a parallelogram is twice the measure of its adjacent angle. Then angles of the parallelogram are

1. ${60}^{\circ }$, ${100}^{\circ }$, ${180}^{\circ }$, ${20}^{\circ }$

2. ${100}^{\circ }$, ${80}^{\circ }$, ${100}^{\circ }$, ${80}^{\circ }$

3. ${140}^{\circ }$, ${20}^{\circ }$, ${120}^{\circ }$, ${80}^{\circ }$

4. ${60}^{\circ }$, ${120}^{\circ }$, ${60}^{\circ }$, ${120}^{\circ }$

Q. Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{7x-2y}{xy}=5$

Q. Solve the following pair of equations. $25x-24y=197;24x-25y=195$

1. $x=9,y=-3$
2. $x=5,y=-3$
3. $x=1,y=-3$
4. $x=3,y=-3$

Q. $\text{Given that}y=\frac{(cx+d)}{b}$;

$\text{where}b\ne 0\&(a+c)\ne 0$,

$\text{then, what is the value of}x,\text{if}ax+by+c=0?$

1. $\frac{(d+c)}{(a+c)}$
2. $\frac{(-d-c)}{(a+c)}$
3. $\frac{(a+c)}{(d+c)}$
4. None

Q.

Question 1 (iv)
Solve the following pair of linear equations by the elimination method and the substitution method:
$\frac{x}{2}+\frac{2y}{3}=-1$ and $x-\frac{y}{3}=3$

Q. $\text{Given that}y=\frac{(cx+d)}{b}$;

$\text{where}b\ne 0\&(a+c)\ne 0$,

$\text{then, what is the value of}x,\text{if}ax+by+c=0?$

Q.

Fill in the blanks:

$3m+4=1$ is a linear equation in___________ variable.