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Page 1 Linear Equations in Two Variables Practice Set 1.1 Q. 1. Complete the following activity to solve the simultaneous equations. 5x + 3y = 9 ……. (i) 2x + 3y = 12 ……… (ii) Answer : 5x + 3y = 9 ……. (i) 2x + 3y = 12 ……… (ii) Subtracting equation (ii) from (i), we get, (5x + 3y ) - (2x + 3y) = 9 - 125x - 2x + 3y - 3y = -33x = -3x = -1Putting the value of x in equation (i), 5(-1) + 3y = 9-5 + 3y = 93y = 14y = 14/3 Let’s add equations (I) and (II). Hence, x = -1 and y = 14/3 is the solution of the equation. Q. 2 A. Solve the following simultaneous equation. 3a + 5b = 26; a + 5b = 22 Answer : Change the sign of Eq. (II) Page 2 Linear Equations in Two Variables Practice Set 1.1 Q. 1. Complete the following activity to solve the simultaneous equations. 5x + 3y = 9 ……. (i) 2x + 3y = 12 ……… (ii) Answer : 5x + 3y = 9 ……. (i) 2x + 3y = 12 ……… (ii) Subtracting equation (ii) from (i), we get, (5x + 3y ) - (2x + 3y) = 9 - 125x - 2x + 3y - 3y = -33x = -3x = -1Putting the value of x in equation (i), 5(-1) + 3y = 9-5 + 3y = 93y = 14y = 14/3 Let’s add equations (I) and (II). Hence, x = -1 and y = 14/3 is the solution of the equation. Q. 2 A. Solve the following simultaneous equation. 3a + 5b = 26; a + 5b = 22 Answer : Change the sign of Eq. (II) Substituting a = 2 in Eq. (II) ? solution is (a, b) = (2, 4) Q. 2 B. Solve the following simultaneous equation. x + 7y = 10; 3x – 2y = 7 Answer : Multiply Eq. I by 2 and Eq. II by 7 x=3 Substituting x= 3 in Eq. I Page 3 Linear Equations in Two Variables Practice Set 1.1 Q. 1. Complete the following activity to solve the simultaneous equations. 5x + 3y = 9 ……. (i) 2x + 3y = 12 ……… (ii) Answer : 5x + 3y = 9 ……. (i) 2x + 3y = 12 ……… (ii) Subtracting equation (ii) from (i), we get, (5x + 3y ) - (2x + 3y) = 9 - 125x - 2x + 3y - 3y = -33x = -3x = -1Putting the value of x in equation (i), 5(-1) + 3y = 9-5 + 3y = 93y = 14y = 14/3 Let’s add equations (I) and (II). Hence, x = -1 and y = 14/3 is the solution of the equation. Q. 2 A. Solve the following simultaneous equation. 3a + 5b = 26; a + 5b = 22 Answer : Change the sign of Eq. (II) Substituting a = 2 in Eq. (II) ? solution is (a, b) = (2, 4) Q. 2 B. Solve the following simultaneous equation. x + 7y = 10; 3x – 2y = 7 Answer : Multiply Eq. I by 2 and Eq. II by 7 x=3 Substituting x= 3 in Eq. I 7y=7 y=1 ? Solution is (x , y) = (3, 1) Q. 2 C. Solve the following simultaneous equation. 2x – 3y = 9; 2x + y = 13 Answer : Change the sign of Eq. (II) Substituting y = 1 in Eq. (II) 2x = 13 - 12x = 12x = 6 ? solution is (x, y) = (1,6) Q. 2 D. Solve the following simultaneous equation. 5m – 3n = 19; m – 6n = –7 Page 4 Linear Equations in Two Variables Practice Set 1.1 Q. 1. Complete the following activity to solve the simultaneous equations. 5x + 3y = 9 ……. (i) 2x + 3y = 12 ……… (ii) Answer : 5x + 3y = 9 ……. (i) 2x + 3y = 12 ……… (ii) Subtracting equation (ii) from (i), we get, (5x + 3y ) - (2x + 3y) = 9 - 125x - 2x + 3y - 3y = -33x = -3x = -1Putting the value of x in equation (i), 5(-1) + 3y = 9-5 + 3y = 93y = 14y = 14/3 Let’s add equations (I) and (II). Hence, x = -1 and y = 14/3 is the solution of the equation. Q. 2 A. Solve the following simultaneous equation. 3a + 5b = 26; a + 5b = 22 Answer : Change the sign of Eq. (II) Substituting a = 2 in Eq. (II) ? solution is (a, b) = (2, 4) Q. 2 B. Solve the following simultaneous equation. x + 7y = 10; 3x – 2y = 7 Answer : Multiply Eq. I by 2 and Eq. II by 7 x=3 Substituting x= 3 in Eq. I 7y=7 y=1 ? Solution is (x , y) = (3, 1) Q. 2 C. Solve the following simultaneous equation. 2x – 3y = 9; 2x + y = 13 Answer : Change the sign of Eq. (II) Substituting y = 1 in Eq. (II) 2x = 13 - 12x = 12x = 6 ? solution is (x, y) = (1,6) Q. 2 D. Solve the following simultaneous equation. 5m – 3n = 19; m – 6n = –7 Answer : Multiply Eq. II by 5 equating (I) and (III), change the sign of Eq. (III) Adding both we get ? n = 2 Substituting n = 2 in Eq 1 ? 5m - 3(2) = 19 ? 5m - 6 = 19 ? 5m = 25 ? m = 5 ? Solution is (m , n) = (5, 2) Q. 2 E. Solve the following simultaneous equation. 5x + 2y = –3; x + 5y = 4 Answer : Multiply Eq. I by 5 and Eq. II by 2 Page 5 Linear Equations in Two Variables Practice Set 1.1 Q. 1. Complete the following activity to solve the simultaneous equations. 5x + 3y = 9 ……. (i) 2x + 3y = 12 ……… (ii) Answer : 5x + 3y = 9 ……. (i) 2x + 3y = 12 ……… (ii) Subtracting equation (ii) from (i), we get, (5x + 3y ) - (2x + 3y) = 9 - 125x - 2x + 3y - 3y = -33x = -3x = -1Putting the value of x in equation (i), 5(-1) + 3y = 9-5 + 3y = 93y = 14y = 14/3 Let’s add equations (I) and (II). Hence, x = -1 and y = 14/3 is the solution of the equation. Q. 2 A. Solve the following simultaneous equation. 3a + 5b = 26; a + 5b = 22 Answer : Change the sign of Eq. (II) Substituting a = 2 in Eq. (II) ? solution is (a, b) = (2, 4) Q. 2 B. Solve the following simultaneous equation. x + 7y = 10; 3x – 2y = 7 Answer : Multiply Eq. I by 2 and Eq. II by 7 x=3 Substituting x= 3 in Eq. I 7y=7 y=1 ? Solution is (x , y) = (3, 1) Q. 2 C. Solve the following simultaneous equation. 2x – 3y = 9; 2x + y = 13 Answer : Change the sign of Eq. (II) Substituting y = 1 in Eq. (II) 2x = 13 - 12x = 12x = 6 ? solution is (x, y) = (1,6) Q. 2 D. Solve the following simultaneous equation. 5m – 3n = 19; m – 6n = –7 Answer : Multiply Eq. II by 5 equating (I) and (III), change the sign of Eq. (III) Adding both we get ? n = 2 Substituting n = 2 in Eq 1 ? 5m - 3(2) = 19 ? 5m - 6 = 19 ? 5m = 25 ? m = 5 ? Solution is (m , n) = (5, 2) Q. 2 E. Solve the following simultaneous equation. 5x + 2y = –3; x + 5y = 4 Answer : Multiply Eq. I by 5 and Eq. II by 2 Change sign of Eq.(IV) Subsituting x=–1in Eq.II ? solution is (x, y) = (–1, 1) Q. 2 F. Solve the following simultaneous equation. Answer :Read More
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FAQs on Textbook Solutions: Linear Equations in Two Variables - Mathematics Class 10 (Maharashtra SSC Board)
| 1. What are linear equations in two variables? |  |
Ans. Linear equations in two variables are mathematical expressions that represent a straight line when graphed on a coordinate plane. They can be written in the standard form Ax + By + C = 0, where A, B, and C are constants, and x and y are the variables. The solutions to these equations are the points (x, y) that lie on the line.
| 2. How can I graph a linear equation in two variables? | |
Ans. To graph a linear equation in two variables, first, rearrange the equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Start by plotting the y-intercept on the graph, then use the slope to find another point. Draw a straight line through these points to represent the equation.
| 3. What methods can be used to solve linear equations in two variables? | |
Ans. There are several methods to solve linear equations in two variables, including the substitution method, elimination method, and graphical method. In the substitution method, one variable is expressed in terms of the other and substituted into the second equation. In the elimination method, equations are manipulated to eliminate one variable, making it easier to solve for the other.
| 4. What is the significance of the solutions of linear equations in two variables? | |
Ans. The solutions of linear equations in two variables represent the points of intersection of two lines on a graph. If the lines intersect at a single point, there is a unique solution. If the lines are parallel, there is no solution. If the lines coincide, there are infinitely many solutions. Understanding these relationships is crucial in various fields, including economics and engineering.
| 5. How can I identify whether a given set of points is a solution to a linear equation in two variables? | |
Ans. To determine if a given set of points is a solution to a linear equation in two variables, substitute the x and y coordinates of each point into the equation. If the left-hand side of the equation equals the right-hand side after substitution, then the point is a solution to the equation. If not, the point does not satisfy the equation.
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