The values of x and y which satisfy the equations: 47x + 31y = 63 and 31x + 47y = 15 are ____________
Given pair of linear equations:
47x+31y = 63 ---(1)
31x+47y = 15 ---(2)
multiply equation (1) by 31 and equation (2) by 47
substract (2) from (1) we get
(961 - 2209)y = 63x31 - 15x47
-1248 y = 1953 - 705
-1248 y = 1248
Therefore, y = -1.
Substitute y = -1 in equation (1) we get
47x = 94
So, x = 2.
Hence, The values of x and y are 2, -1.
If x + 2y = 5 & x – 2y = 7, then the value of x & y is: -
A train overtakes two persons who are walking at the rate of 8 kmph and 12 kmph in the same direction in which the train is going, and passes them completely in 9 and 10 seconds respectively. What is the length of the train?
Adding 1 to the numerator and subtracting 1 from the denominator of a fraction makes it 1. However, if 1 is added only to the denominator of the fraction it becomes ½ . The fraction is______
In elimination method _____________ is an important condition.
In the elimination method we equate either of the coefficient so that the other is eliminated ,substituting the value of one variable into the other equation and then we are left with the linear equation which is solvable and values of the variables are obtained.
The value of x in mx + ny = c; nx – ny = c + 1 is
The sum of the digits of a two digit number is 12. The number obtained by reversing its digits exceeds the given number by 18. Then the number is_____
Let us assume x and y are the two digits of the number
Therefore, two-digit number is = 10x + y and the reversed number = 10y + x
x + y = 12
y = 12 – x (1)
10y + x - 10x – y = 18
9y – 9x = 18
y – x = 2 (2)
Substitute the value of y from Equation 1 in Equation 2
12 – x – x = 2
12 – 2x = 2
2x = 10
x = 5
Therefore, y = 12 – x = 12 – 5 = 7
Therefore, the two-digit number is 10x + y = (10*5) + 7 = 57
If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b are, respectively.
Given, x=a and y=b.
Given equations, x-y=2( assume it as equation 1)
x+y=4( assume it as equation 2)
- - - - - - -
2x=6( y gets cancelled as there is a negative y and a positive y implies y-y=0)
But x=a implies a=3
substitute a in equation 1 (it can be substituted even in equation 2)
But y=b implies b=1
Therefore, a=3 and b=1
A lending library has a fixed charge for the first two days and an additional charge for each day thereafter. Sunil paid Rs 28 for a book kept for seven days, while Sohail paid Rs 32 for the book he kept for nine days. Find the charge for each extra day.
At a closing down sale, a book store was selling 3 books and 5 notebooks for Rs 309 or 6 books and 2 notebooks for Rs 282. How much would one book and 1 notebook cost?