Advertisements
Advertisements
Question
Solve the following simultaneous equation.
2x + y = -2 ; 3x - y = 7
Advertisements
Solution
2x + y = -2 ...(I)
3x - y = 7 ...(II)
Adding (I) and (II)
5x = 5
⇒ x = 1
Putting the value of x in (I)
2 × 1 + y = -2
⇒ 2 + y = -2
⇒ y = - 4
APPEARS IN
RELATED QUESTIONS
Solve the following system of equations: 15x + 4y = 61; 4x + 15y = 72
Solve the following system of equations by using the method of elimination by equating the co-efficients.
`\frac { x }{ y } + \frac { 2y }{ 5 } + 2 = 10; \frac { 2x }{ 7 } – \frac { 5 }{ 2 } + 1 = 9`
Solve the following system of linear equations by using the method of elimination by equating the coefficients √3x – √2y = √3 = ; √5x – √3y = √2
Solve the following pair of linear equation by the elimination method and the substitution method:
3x + 4y = 10 and 2x – 2y = 2
Solve the following pair of linear equation by the elimination method and the substitution method.
3x – 5y – 4 = 0 and 9x = 2y + 7
Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
Two types of boxes A, B are to be placed in a truck having a capacity of 10 tons. When 150 boxes of type A and 100 boxes of type B are loaded in the truck, it weighes 10 tons. But when 260 boxes of type A are loaded in the truck, it can still accommodate 40 boxes of type B, so that it is fully loaded. Find the weight of each type of box.
Sanjay gets fixed monthly income. Every year there is a certain increment in his salary. After 4 years, his monthly salary was Rs. 4500 and after 10 years his monthly salary became 5400 rupees, then find his original salary and yearly increment.
Ajay is younger than Vijay by 5 years. Sum of their ages is 25 years. What is Ajay's age?
By equating coefficients of variables, solve the following equations.
3x - 4y = 7; 5x + 2y = 3
By equating coefficients of variables, solve the following equation.
5x + 7y = 17 ; 3x - 2y = 4
By equating coefficients of variables, solve the following equation.
x − 2y = −10 ; 3x − 5y = −12
Complete the activity.
Complete the following table to draw the graph of 3x – 2y = 18.
| x | 0 | 4 | 2 | –1 |
| y | –9 | ______ | ______ | ______ |
| (x, y) | (0, −9) | (______, _______) | (______, _______) | ______ |
Difference between two numbers is 3. The sum of three times the bigger number and two times the smaller number is 19. Then find the numbers.
The semi perimeter of a rectangular shape garden is 36 m. The length of the garden is 4 m more than its breadth. Find the length and the breadth of the garden.
The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.
The angles of a cyclic quadrilateral ABCD are ∠A = (6x + 10)°, ∠B = (5x)°, ∠C = (x + y)°, ∠D = (3y – 10)°. Find x and y, and hence the values of the four angles.
Read the following passage:
Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 Students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively. |
Based on the above information, answer the following questions:
- Represent the following information algebraically (in terms of x and y).
- (a) What is the prize amount for hockey?
OR
(b) Prize amount on which game is more and by how much? - What will be the total prize amount if there are 2 students each from two games?
