Advertisements
Advertisements
Question
By equating coefficients of variables, solve the following equation.
5x + 7y = 17 ; 3x - 2y = 4
Advertisements
Solution
5x + 7y = 17 ...(I)
3x - 2y = 4 ...(II)
Multiply (I) with 3 and (II) with 5
15x + 21y = 51 ...(III)
15x - 10y = 20 ...(IV)
Subtracting (IV) from (III) we get,
15x + 21y = 51
15x - 10y = 20
- + -
31y = 31
⇒ y = 1
Putting this value of y in (I) we get
∴ 5x + 7y = 17
5x + 7 × 1 = 17
⇒ 5x = 10
⇒ x = 2
Thus, x = 2, y = 1
APPEARS IN
RELATED QUESTIONS
Solve the following system of linear equations by using the method of elimination by equating the coefficients: 3x + 4y = 25 ; 5x – 6y = – 9
Solve the following pair of linear equation by the elimination method and the substitution method.
3x – 5y – 4 = 0 and 9x = 2y + 7
Solve the following pair of linear equation by the elimination method and the substitution method.
`x/2 + (2y)/3 = -1 and x - y /3 = 3`
Form the pair of linear equation in the following problem, and find its solutions (if they exist) by the elimination method:
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
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.
Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:
Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received.
The sum of a two-digit number and the number formed by reversing the order of digit is 66. If the two digits differ by 2, find the number. How many such numbers are there?
In an envelope there are some 5 rupee notes and some 10 rupee notes. Total amount of these notes together is 350 rupees. Number of 5 rupee notes are less by 10 than twice number of 10 rupee notes. Then find the number of 5 rupee and 10 rupee notes.
If the length of a rectangle is reduced by 5 units and its breadth is increased by 3 units, then the area of the rectangle is reduced by 9 square units. If length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 67 square units. Then find the length and breadth of the rectangle.
Solve the following simultaneous equation.
2x - y = 5 ; 3x + 2y = 11
Solve the following simultaneous equation.
`x/3 + 5y = 13 ; 2x + y/2 = 19`
By equating coefficients of variables, solve the following equations.
3x - 4y = 7; 5x + 2y = 3
By equating coefficients of variables, solve the following equation.
x − 2y = −10 ; 3x − 5y = −12
The difference between an angle and its complement is 10° find measure of the larger angle.
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) | (______, _______) | (______, _______) | ______ |
Solve: 99x + 101y = 499; 101x + 99y = 501
The length of the rectangle is 5 more than twice its breadth. The perimeter of a rectangle is 52 cm, then find the length of the rectangle.
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is ______.
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.
