Maharashtra Board 10th Class Maths Part 1 Practice Set 1.4 Solutions Chapter 1 Linear Equations in Two Variables

Balbharti Maharashtra State Board Class 10 Maths Solutions covers the Practice Set 1.4 Algebra 10th Class Maths Part 1 Answers Solutions Chapter 1 Linear Equations in Two Variables.

Practice Set 1.4 Algebra 10th Std Maths Part 1 Answers Chapter 1 Linear Equations in Two Variables

Question 1.
Solve the following simultaneous equations.
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 1
Solution:
i. The given simultaneous equations are
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 2
∴ Equations (i) and (ii) become
2p – 3q = 15 …(iii)
8p + 5q = 77 …(iv)
Multiplying equation (iii) by 4, we get
8p – 12q = 60 …(v)
Subtracting equation (v) from (iv), we get
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 3
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 4

ii. The given simultaneous equations are
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 5
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 6
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 7
Substituting x = 3 in equation (vi), we get
3 + y = 5
∴ y = 5 – 3 = 2
∴ (x, y) = (3, 2) is the solution of the given simultaneous equations.

iii. The given simultaneous equations are
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 8
∴ Equations (i) and (ii) become
27p + 31q = 85 …(iii)
31p + 27q = 89 …(iv)
Adding equations (iii) and (iv), we get
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 9
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 10
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 11

iv. The given simultaneous equations are
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 12
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 13
Substituting x = 1 in equation (vi), we get
3(1) + y = 4
∴ 3 + y = 4
∴ y = 4 – 3 = 1
∴ (x, y) = (1, 1) is the solution of the given simultaneous equations.

Question 1.
Complete the following table. (Textbook pg. no. 16)
Solution:
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 14

Question 2.
In the above table the equations are not linear. Can you convert the equations into linear equations? (Textbook pg. no. 17)
Answer:
Yes, the above given simultaneous equations can be converted to a pair of linear equations by making suitable substitutions.

Steps for solving equations reducible to a pair of linear equations.

  • Step 1: Select suitable variables other than those which are in the equations.
  • Step 2: Replace the given variables with new variables such that the given equations become linear equations in two variables.
  • Step 3: Solve the new simultaneous equations and find the values of the new variables.
  • Step 4: By resubstituting the value(s) of the new variables, find the replaced variables which are to be determined.

Question 3.
To solve given equations fill the below boxes suitably. (Text book pg.no. 19)
Answer:
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 15

Question 4.
The examples on textbook pg. no. 17 and 18 obtained by transformation are solved by elimination method. If you solve these equations by graphical method and by Cramer’s rule will you get the same answers? Solve and check it. (Textbook pg. no. 18)
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 16
Solution:
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 17 Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 18
The two lines intersect at point (1,-1).
∴ p = 1 and q = -1 is the solution of the simultaneous equations 4p + q = 3 and 2p – 3q = 5.
Re substituting the values of p and q, we get
Maharashtra Board Class 10 Maths Solutions Chapter 1 Linear Equations in Two Variables Practice Set Ex 1.4 19
The two lines intersect at point (0, -1).
∴ x = 0 and y = -1 is the solution of the simultaneous equations x – y = 1 and x + y = -1.
∴ (x, y) = (0, -1) is the solution of the given simultaneous equations.

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