Advertisements
Advertisements
प्रश्न
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`
Advertisements
उत्तर
`x/2 + (2y)/3 = - 1` and `x - y/3 = 3`
By elimination method
`x/2 + (2y)/3 = -`1 ...(i)
`x-y/3 = 3` ...(ii)
Multiplying equation (i) by 2, we get
`x + (4y)/3 = - 2` ...(iii)
Subtracting equation (ii) from equation (iii), we get
`(5y)/3 = -5`
Dividing by 5 and multiplying by 3, we get
`y = -15/5`
y = -3
Putting this value in equation (ii), we get
`x - y/3 = 3` ...(ii)
`x-(-3)/3 = 3`
x + 1 = 3
x = 2
Hence, our answer is x = 2 and y = −3.
By substitution method
`x - y/3 = 3` ...(ii)
Add `y/3` both side, we get
`x = 3 + y/3` ...(iv)
Putting this value in equation (i), we get
`x/2 + (2y)/3 = - 1` ...(i)
`(3+ y/3)/2 + (2y)/3 = -1 `
`3/2 + y/6 + (2y)/3 = - 1`
Multiplying by 6, we get
9 + y + 4y = - 6
5y = -15
y = - 3
Hence, our answer is x = 2 and y = −3.
APPEARS IN
संबंधित प्रश्न
Solve the following system of equations: 15x + 4y = 61; 4x + 15y = 72
Solve the following pair of linear equation by the elimination method and the substitution method:
x + y = 5 and 2x – 3y = 4
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.
The sum of the digits in a two-digits number is 9. The number obtained by interchanging the digits exceeds the original number by 27. Find the two-digit number.
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.
x + y = 11 ; 2x - 3y = 7
Solve the following simultaneous equation.
`x/3 + y/4 = 4; x/2 - y/4 = 1`
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
By equating coefficients of variables, solve the following equation.
4x + y = 34 ; x + 4y = 16
If 52x + 65y = 183 and 65x + 52y = 168, then find x + y = ?
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) | (______, _______) | (______, _______) | ______ |
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 solution of the equation ax + by + 5 = 0 and bx − ay − 12 = 0 is (2, – 3). Find the values of a and b
Rehana went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Rehana got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 did she received.
