Activity : complete the following Table.

NO.	Equation	Is the equationa linear equation in 2 variables
1	4m + 3n = 12	Yes
2	3x² - 7y = 13	No
3	√2 x - √5 y = 16	Yes
4	0x + 6y - 3 = 0	No
5	0.3x + 0y -36 = 0	No
6	4/x + 5/y = 4	Yes
7	4xy - 5y - 8 = 0	NO

Ex (2) Solve : 3x + 2y = 29 ; 5x - y = 18
Solution : 3x + 2y = 29. . . (I) and 5x - y = 18. . . (II)

Let's solve the equations by eliminating 'y' . Fill suitably the boxes below.↓
Multiplying equation (II) by 2.

∴ 5x × 2 - y × 2 = 18 × 2
∴ 10x - 2y = 36 . . . (III)

Let's add equations (I) and (III)

3x + 2y = 29
+10x - 2y = +36
________________________

13x = 65 → ∴ x = 5
Substituting x = 5 in equation (I)

3x + 2y = 29
∴ 3 × 5 + 2y = 29
∴ 15 + 2y = 29
∴ 2y = 29 - 15
∴ 2y = 6 → ∴ y = 3
(x,y) = ( 5,3 ) is the solⁿ

Practice Set 1.1

Q.1 Complete the following Activity to solve the simultaneous equation

5x + 3y = 9 - - - - - (I)
2x - 3y = 12 - - - - - (II)

Let's add equation (I) and (II)

5x + 3y = 9
+
2x - 3y = 12
________________________
7 x = 21
x = 3

Place x = 3 in equation (I).
5 × 3 + 3y = 9
3y = 9 - 15
3y = -6
y = -2
∴Solution is (x,y) = ( 3 , -2 )

Q. 2 solve the following simultaneous equation

1. 3a + 5b = 26 ; a + 5b = 22

solⁿ : 3a + 5b = 26 . . . . (I) ; a + 5b = 22 . . . . (II)

subtracting equation (I) and (II)

3a + 5b = 26
-
a - 5b = -22
________________________
2a = 4 → ∴ a = 2

Put value of a in equation (I)
∴ 3 × 2 + 5b = 26
∴ 5b = 26 - 6
∴ b = 4

2. x + 7y = 10 ; 3x - 2y = 7

solⁿ : x + 7y = 10 . . . . (I) ; 3x - 2y = 7 . . . . (II)

Multiplying 3 by equation (I)

3x + 21y = 30 . . . . (III)

subtracting equation (II) and (III)

3x + 21y = 30
-
-3x +2y = -7
________________________
23y = 23 → ∴ y = 1

Put value of y in equation (I)
∴ x + 7 × 1 = 10
∴ x = 10 - 7
∴ x = 3

3. 1/3x + y = 10/3 ; 2x - 1/4y = 11/4

solⁿ : 1/3x + y = 10/3 . . . . (I) ; 2x - 1/4y = 11/4 . . . . (II)

Multiplying 1/4 to equation (I)

7/12x + 1/4y = 43/12 . . . . (III)

Adding equation (II) and (III)

7/12x + 1/4y = 43/12
+
2x - 1/4y = 11/4
________________________
19/12x = 76/12 → ∴ x = 4

Put value of x in equation (I)
∴ 1/3 × 4 + y = 10/3
∴ y = 10/3 - 13/3
∴ y = -1

4. 99x + 101y = 499 ; 101x - 99y = 501

solⁿ : 99x + 101y = 499 . . . . (I) ; 101x - 99y = 501 . . . . (II)

Adding equation (I) and (II)

99x + 101y = 499
+
101x - 99y = 501
________________________
200x + 200y = 1000

200(x+y) = 1000

x + y = 5 . . . . (III)

subtracting equation (I) and (II)

99x + 101y = 499
-
101x + 99y = -501
________________________
2x - 2y = 2

2(x-y) = 2

x - y = 2 . . . . (IV)

Adding equation (III) and (IV)
x = 3
put x in (III)
3 + y = 5
∴ y = 2

Activity : complete the following Table.

x - y = 1

x	0	1	3	-2
y	-1	0	2	-3
(x,y)	0,-1	1,0	3,-2	-2,-3

Activity : complete the following Table.

5x - 3y = 1

x	2	5	-1	-4
y	3	8	-2	-7
(x,y)	2,3	5,8	-1,-2	-4,-7

Practice set 1.2

Q.1 Complete the following table to draw graph of the equation

1. x + y = 3

x	3	-2	0
y	0	5	3
(x,y)	3,0	-2,5	0,3

2. x - y = 4

x	3	-2	0
y	0	5	3
(x,y)	3,0	-2,5	0,3

Q. 2 solve the following simultaneous equation graphically

1. x + y = 6

x	0	6	2
y	6	0	4
(x,y)	0,6	6,0	2,4

x - y = 4

x	4	5	0
y	0	1	-4
(x,y)	4,0	5,1	0,-4

Point of intersection of the two lines is (5, 1).

6.. 2x -3y = 4

x	2	3.5	1
y	0	1	-0.6
(x,y)	2,0	3.5,1	1,-0.6

3y - x = 4

x	-4	2	-1
y	0	2	1
(x,y)	-4,0	2,2	-1,1

Point of intersection of the two lines is (8 , 4).

If you want all solⁿ of this simultaneous equation .

click below link ↓
All solⁿ

Activity : To solve the simultaneous equation by determinate method , fill in the blanks.

y + 2x - 19 = 0 ; 2x - 3y + 3 = 0

solution : write the given equation in the form ax + by = c

2x + y = 19
2x - 3y = -3

Activity 2 : Complete the following avtivity.

3x - 2y = 3
2x + y = 16

solution :

$D = | \begin{matrix} 3 & - 2 \\ 2 & 1 \end{matrix} | = 3 (1) - 2 (- 2) = 7$

$D_{x} = | \begin{matrix} 3 & - 2 \\ 16 & 1 \end{matrix} |$ = 3(1) - 16(-2) = 3 + 32 = 35

$D_{y} = | \begin{matrix} 3 & 3 \\ 2 & 16 \end{matrix} |$ = 3(16) - 3(2) = 48 - 6 = 42

Now,

$x = \frac{D_{x}}{D}$ $y = \frac{D_{y}}{D}$

$x = \frac{35}{7}$ $y = \frac{42}{7}$

x = 5 y = 6

Practice Set 1.3

Q.1 Fill in the blanks with correct nunber

Fill in the blanks with correct number $| \begin{matrix} 3 & 2 \\ 4 & 5 \end{matrix} |$ = 3 x ____ - ____ x 4 = ____ - 8 = ____

click here for sol → Solution

Solve the following simultaneous equations using Cramer’s rule.

(1.) 3x – 4y = 10 ; 4x + 3y = 5

Sol :

Given equations,

3x – 4y = 10
4x + 3y = 5

D = $| \begin{matrix} 3 & - 4 \\ 4 & 3 \end{matrix} | = 3 \times 3 - (- 4) \times 4 = 9 + 16 = 25$

D_x = $| \begin{matrix} 10 & - 4 \\ 5 & 3 \end{matrix} | = 10 \times 3 - (- 4) \times 5 = 30 + 20 = 50$

D_y = $| \begin{matrix} 3 & 10 \\ 4 & 5 \end{matrix} | = 3 \times 5 - 10 \times 4 = 15 - 40 = - 25$

By using cramer's rule,

x = $\frac{D_{x}}{D} = \frac{50}{25} = 2$

y = $\frac{D_{y}}{D} = \frac{- 25}{25} = - 1$

(x, y) = (2, –1) is the solution.

(2.) 4x + 3y – 4 = 0 ; 6x = 8 – 5y

Sol :

4x + 3y – 4 = 0

6x = 8 – 5y

Write the given equations in the form ax + by = c
4x + 3y = 4
6x + 5y = 8

D = $| \begin{matrix} 4 & 3 \\ 6 & 5 \end{matrix} | = 4 \times 5 - 3 \times 6 = 20 - 18 = 2$

D_x = $| \begin{matrix} 4 & 3 \\ 8 & 5 \end{matrix} | = 4 \times 5 - 3 \times 8 = 20 - 24 = - 4$

D_y = $| \begin{matrix} 4 & 4 \\ 6 & 8 \end{matrix} | = 4 \times 8 - 4 \times 6 = 32 - 24 = 8$

By using Cramer’s Rule,

x = $\frac{D_{x}}{D} = \frac{- 4}{2} = - 2$

x = $\frac{D_{y}}{D} = \frac{8}{2} = 4$

(x, y) = (-2, 4) is the solution of the given equations.

( 6) 2x + 3y = 2; x - $\frac{y}{2} = \frac{1}{2}$ .

Sol :

2x + 3y = 2; x -

\frac{y}{2} = \frac{1}{2}

D =

| \begin{matrix} 2 & 3 \\ 1 & \frac{- 1}{2} \end{matrix} | = 2 \times (- \frac{1}{2}) - 3 \times 1 = - 1 - 3 = - 4

D_x =

| \begin{matrix} 2 & 3 \\ \frac{1}{2} & \frac{- 1}{2} \end{matrix} | = 2 \times (- \frac{1}{2}) - 3 \times \frac{1}{2} = - 1 - \frac{3}{2} = \frac{- 5}{2}

D_y =

| \begin{matrix} 2 & 2 \\ 1 & \frac{1}{2} \end{matrix} | = 2 \times \frac{1}{2} - 2 \times 1 = 1 - 2 = - 1

x =

\frac{D_{x}}{D} = \frac{\frac{- 5}{2}}{- 4} = \frac{5}{8} .

y =

\frac{D_{y}}{D} = \frac{- 1}{- 4} = \frac{1}{4} .

(x, y) =

(\frac{5}{8}, \frac{1}{4})

click link for all solution of this parctice set ↓

Activity : Complete the following table.

Sol :

Activity : To solve the given equation fill the boxes below suitably.

∴ (x, y) = (4, 5) is the solution of the given simultaneous equation.

Practice Set 1.4

Solve the simultaneous equations

(1.)

\frac{2}{x} - \frac{3}{y} = 15; \frac{8}{x} + \frac{5}{y} = 77

Sol :

\frac{2}{x} - \frac{3}{y} = 15; \frac{8}{x} + \frac{5}{y} = 77

Let \frac{1}{x} = u and \frac{1}{y} = v

So, the equation becomes

2 u - 3 v = 15 . . . . . (I)

8 u + 5 v = 77 . . . . . (I I)

Multiply (I) with 4 we get

8 u - 12 v = 60 . . . . . (I I I)

(II) − (III)

8 u - 8 u + 5 v - (- 12 v) = 77 - 60

\Rightarrow 17 v = 17

\Rightarrow v = 1

Putting the value of v in (I)

2 u - 3 (1) = 15

\Rightarrow 2 u = 15 + 3 = 18

\Rightarrow u = 9

Thus,

\frac{1}{x} = u = 9

\Rightarrow x = \frac{1}{9}

\frac{1}{y} = v = 1

\Rightarrow y = 1

(x, y) = (\frac{1}{9}, 1)

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CHAPTER 1 → Linear equations in Two variables

Practice Set 1.1

Q.1 Complete the following Activity to solve the simultaneous equation

Q. 2 solve the following simultaneous equation

Practice set 1.2

Q.1 Complete the following table to draw graph of the equation

Q. 2 solve the following simultaneous equation graphically

If you want all solⁿ of this simultaneous equation .

Practice Set 1.3

Q.1 Fill in the blanks with correct nunber

Practice Set 1.4

Practice Set 1.4

Problem Set - 1

x	-5	x
y	x	0
(x,y)	(-5,x)	(x,0)

Practice Set 1.1

Q.1 Complete the following Activity to solve the simultaneous equation

Q. 2 solve the following simultaneous equation

Practice set 1.2

Q.1 Complete the following table to draw graph of the equation

Q. 2 solve the following simultaneous equation graphically

If you want all soln of this simultaneous equation .

Practice Set 1.3

Q.1 Fill in the blanks with correct nunber

Practice Set 1.4

Practice Set 1.4

Problem Set - 1

If you want all solⁿ of this simultaneous equation .