Balbharati solutions for Algebra (Mathematics 1) [English] 10 Standard SSC Maharashtra State Board chapter 1 - Linear Equations in Two Variables [Latest edition]

Complete the following activity to solve the simultaneous equations.
5x + 3y = 9 -----(I)
2x − 3y = 12 ----- (II)

Solve the following simultaneous equation.

3a + 5b = 26; a + 5b = 22

Solve the following simultaneous equation.

x + 7y = 10; 3x – 2y = 7

Solve the following simultaneous equation.
2x – 3y = 9; 2x + y = 13

Solve the following simultaneous equation.

5m – 3n = 19; m – 6n = –7

Solve the following simultaneous equation.
5x + 2y = –3; x + 5y = 4

Solve the following simultaneous equation.

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

Solve the following simultaneous equation.

99x + 101y = 499; 101x + 99y = 501

Solve the following simultaneous equation.
49x – 57y = 172; 57x – 49y = 252

Complete the following table to draw graph of the equation -

(I) x + y = 3 (II) x – y = 4

x + y = 3

x – y = 4

Solve the following simultaneous equations graphically.

x + y = 6 ; x – y = 4

Solve the following simultaneous equations graphically.
x + y = 5; x – y = 3

Solve the following simultaneous equations graphically.

x + y = 0 ; 2x – y = 9

Solve the following simultaneous equation graphically.

3x – y = 2 ; 2x – y = 3

Solve the Following Simultaneous Equation Graphically.

3x – 4y = –7; 5x – 2y = 0

Solve the following simultaneous equations graphically.

2x – 3y = 4 ; 3y – x = 4

Fill in the blanks with correct number:

`|(3,2),(4,5)| = 3 xx square - square xx 4 = square - 8 = square`

Find the value of following determinant.

`|(-1,7),(2,4)|`

Find the value of following determinant.

`|(5,3), (-7,0)|`

Find the values of following determinant.

`|(7/3,5/3), (3/2, 1/2)|`

Solve the following simultaneous equations using Cramer’s rule.

3x – 4y = 10 ; 4x + 3y = 5

Solve the following simultaneous equations using Cramer’s rule.

4x + 3y – 4 = 0 ; 6x = 8 – 5y

Solve the following simultaneous equations using Cramer’s rule.
x + 2y = –1 ; 2x – 3y = 12

Solve the following simultaneous equations using Cramer’s rule.

6x – 4y = –12; 8x – 3y = –2

Solve the following simultaneous equations using Cramer’s rule.

4m + 6n = 54; 3m + 2n = 28

Solve the following simultaneous equations using Cramer’s rule.
2x + 3y = 2; x - `y/2 = 1/2`.

Solve the following simultaneous equation.

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

Solve the following simultaneous equations.

`10/("x" + "y") + 2/("x" - "y") = 4; 15/("x" + "y") - 5/("x" - "y") = -2`

Solve the following simultaneous equations.

`27/(x -2) + 31/(y + 3) = 85, 31/(x -2) + 27/(y + 3) = 89`

Solve the following simultaneous equation.

`1/(3x + y) + 1/(3x - y) = 3/4; 1/(2(3x + y))  - 1/(2(3x - y))  = -1/8`

Complete the following.

Choose correct alternative for the following question.
To draw graph of 4x + 5y = 19, Find y when x = 1.

Choose correct alternative for the following question.
For simultaneous equations in variables x and y, D_x = 49, D_y = –63, D = 7 then what is x?

Find the value of `|(5,3),(-7,-4)|`.

Choose correct alternative for the following question.

To solve x + y = 3; 3x – 2y – 4 = 0 by determinant method find D.

Choose correct alternative for the following question.
ax + by = c and mx + ny = d and an ≠ bm then these simultaneous equations have -

Complete the following table to draw the graph of 2x – 6y = 3.

Solve the following simultaneous equation graphically.

2x + 3y = 12 ; x – y = 1

Solve the following simultaneous equation graphically.

x – 3y = 1 ; 3x – 2y + 4 = 0

Solve the following simultaneous equation graphically.
5x – 6y + 30 = 0 ; 5x + 4y – 20 = 0

Solve the following simultaneous equation graphically.
3x – y – 2 = 0 ; 2x + y = 8

Solve the following simultaneous equation graphically.
3x + y = 10 ;  x – y = 2

Find the value of the following determinant.

Find the value of the following determinant.

`|(5, -2), (-3, 1)|`

Find the value of the following determinant.

Solve the following equations by Cramer’s method.

6x – 3y = –10 ; 3x + 5y – 8 = 0

Solve the following equation by Cramer’s method.

4m – 2n = –4 ; 4m + 3n = 16

Solve the following equations by Cramer’s method.

`3x  –  2y = 5/2; 1/3x + 3y = -4/3`

Solve the following equations by Cramer’s method.
7x + 3y = 15; 12y – 5x = 39

Solve the following equation by Cramer’s method.

`("x" + "y" - 8)/2 = ("x" + 2y - 14)/3 = (3"x" - "y")/4`

Solve the following simultaneous equation.

\[\frac{2}{x} + \frac{2}{3y} = \frac{1}{6} ; \frac{3}{x} + \frac{2}{y} = 0\]

Solve the following simultaneous equations.

\[\frac{7}{2x + 1} + \frac{13}{y + 2} = 27 ; \frac{13}{2x + 1} + \frac{7}{y + 2} = 33\]

Solve the following simultaneous equation.

Solve the following simultaneous equations.

Solve the following simultaneous equations.

`1/(2(3x + 4y)) + 1/(5(2x - 3y)) = 1/4; 5/(3x + 4y) - 2/(2x - 3y) = (-3)/2`.

Solve the following word problem.
A two-digit number and the number with digits interchanged add up to 143. In the given number the digit in unit’s place is 3 more than the digit in the ten’s place. Find the original number.

Let the digit in unit’s place is x

and that in the ten’s place is y

∴ the number = `square` y + x

The number obtained by interchanging the digits is `square` x + y

According to the first condition two digit number + the number obtained by interchanging the digits = 143

∴ 10y + x + `square` = 143

∴ `square` x + `square` y = 143

x + y = `square` ........(I)

From the second condition,

digit in unit’s place = digit in the ten’s place + 3

∴ x = `square` + 3

∴ x − y = 3 ........(II)

Adding equations (I) and (II)

2x = `square`

x = 8

Putting this value of x in equation (I)

x + y = 13

8 + `square` = 13

∴ y = `square`

The original number is 10 y + x

= `square` + 8

= 58

Kantabai bought \[1\frac{1}{2}\] kg tea and 5 kg sugar from a shop. She paid ₹ 50 as return fare for rickshaw. Total expense was ₹ 700. Then she realised that by ordering online the goods can be bought with free home delivery at the same price. So next month she placed the order online for 2 kg tea and 7 kg sugar. She paid ₹ 880 for that. Find the rate of sugar and tea per kg.

Solve the following word problem.

To find number of notes that Anushka had, complete the following activity.

Solve the Following Word Problem.
Sum of the present ages of Manish and Savita is 31. Manish’s age 3 years ago was 4 times the age of Savita. Find their present ages.

Solve the Following Word Problem.
In a factory the ratio of salary of skilled and unskilled workers is 5 : 3. Total salary of one day of both of them is Rs 720. Find daily wages of skilled and unskilled workers.

Solve the Following Word Problem.
Places A and B are 30 km apart and they are on a st raight road. Hamid travels from A to B on bike. At the same time Joseph starts from B on bike, travels towards A. They meet each other after 20 minutes. If Joseph would have started from B at the same time but in the opposite direction (instead of towards A) Hamid would have caught him after 3 hours. Find the speed of Hamid and Joseph.