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 for x and y : `\frac { ax }{ b } – \frac { by }{ a } = a + b ; ax – by = 2ab`
Solve the following pair of linear equation by the elimination method and the substitution method:
3x + 4y = 10 and 2x – 2y = 2
Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes `1/2` if we only add 1 to the denominator. What is the fraction?
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:
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Out of 1900 km, Vishal travelled some distance by bus and some by aeroplane. The bus travels with an average speed of 60 km/hr and the average speed of the aeroplane is 700 km/hr. It takes 5 hours to complete the journey. Find the distance, Vishal travelled by bus.
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?
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 - 2y = -1 ; 2x - y = 7
Solve the following simultaneous equation.
x − 2y = −2 ; x + 2y = 10
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
A fraction becomes `(1)/(3)` when 2 is subtracted from the numerator and it becomes `(1)/(2)` when 1 is subtracted from the denominator. Find the fraction.
Complete the following table to draw the graph of 3x − 2y = 18
| x | 0 | 4 | 2 | −1 |
| y | − 9 | ______ | ______ | ______ |
| (x, y) | (0, −9) | (______, _______) | (______, _______) | ______ |
The sum of the two-digit number and the number obtained by interchanging the digits is 132. The digit in the ten’s place is 2 more than the digit in the unit’s place. Complete the activity to find the original number.
Activity: Let the digit in the unit’s place be y and the digit in the ten’s place be x.
∴ The number = 10x + y
∴ The number obtained by interchanging the digits = `square`
∴ The sum of the number and the number obtained by interchanging the digits = 132
∴ 10x + y + 10y + x = `square`
∴ x + y = `square` .....(i)
By second condition,
Digit in the ten’s place = digit in the unit’s place + 2
∴ x – y = 2 ......(ii)
Solving equations (i) and (ii)
∴ x = `square`, y = `square`
Ans: The original number = `square`
The solution of the equation ax + by + 5 = 0 and bx − ay − 12 = 0 is (2, – 3). Find the values of a and b
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.
