Advertisements
Advertisements
Question
If 15x + 17y = 21 and 17x + 15y = 11, then find the value of x + y.
Solution
The given equations are
15x + 17y = 21 ...(1)
17x + 15y = 11 ...(2)
Adding equations (1) and (2)
15x + 17y = 21
+ 17x + 15y = 11
32x + 32y = 32
Dividing both sides by 32, we get
∴ x + y = 1
APPEARS IN
RELATED QUESTIONS
In the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:
3x - 5y = 20
6x - 10y = 40
Find the value of k for which each of the following systems of equations has infinitely many solutions :
2x + 3y − 5 = 0
6x + ky − 15 = 0
Obtain the condition for the following system of linear equations to have a unique solution
ax + by = c
lx + my = n
Determine the values of a and b so that the following system of linear equations have infinitely many solutions:
(2a - 1)x + 3y - 5 = 0
3x + (b - 1)y - 2 = 0
Solve for x and y:
`9/x - 4/y = 8, (13)/x + 7/y = 101`
Solve for x and y:
`x/a + y/b = 2, ax – by = (a^2 – b^2)`
Solve for x and y:
`x + y = a + b, ax - by = a^2 - b^2`
Find the value of k for which the system of equations has a unique solution:
4x + ky + 8=0,
x + y + 1 = 0.
Find the value of k for which the system of equations has a unique solution:
kx + 3y = (k – 3),
12x + ky = k
Find the values of a and b for which the system of linear equations has an infinite number of solutions:
(2a – 1) x + 3y = 5, 3x + (b – 1)y = 2.
The difference between two numbers is 14 and the difference between their squares is 448. Find the numbers.
The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.
A number consisting of two digits is seven times the sum of its digits. When 27 is subtracted from the number, the digits are reversed. Find the number.
The sum of the numerator and denominator of a fraction is 8. If 3 is added to both of the numerator and the denominator, the fraction becomes `3/4`. Find the fraction.
Find a fraction which becomes `(1/2)` when 1 is subtracted from the numerator and 2 is added to the denominator, and the fraction becomes `(1/3)` when 7 is subtracted from the numerator and 2 is subtracted from the denominator.
The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3. They are in the ratio of 2: 3. Determine the fraction.
A man sold a chair and a table together for Rs. 1520, thereby making a profit of 25% on chair and 10% on table. By selling them together for Rs. 1535, he would have made a profit of 10% on the chair and 25% on the table. Find the cost price of each.
Abdul travelled 300 km by train and 200 km by taxi taking 5 hours and 30 minutes. But, if he travels 260km by train and 240km by taxi, he takes 6 minutes longer. Find the speed of the train and that of taxi.
Show that the system 2x + 3y -1= 0 and 4x + 6y - 4 = 0 has no solution.
a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, where a1, b1, c1, a2, b2, c2 are all real numbers and a12+ b12 ≠ 0, a22 + b22 ≠ 0, is called a ______.
