How many integral values of x and y satisfy the equation 5x + 9y = 7, where -500 < x < 500 and -500 < y < 500?

How many integral values of x and y satisfy the equation 5x + 9y = 7, where -500 < x < 500 and -500 < y < 500? Correct Answer 111

Given:

x and y satisfy the equation 5x + 9y = 7

Formula Used:

In A.P. 

Last term(l) = First term(a) + ⋅Common difference(d)

l = a + (n - 1)d

Then n = + 1

Calculation:

We need to find those integer values of x which will give integer values of y when we put them in the equation.

Put x = -1 y = 12/9 (Not an integer)

Put x = -2 y = 17/9 (Not an integer)

Put x = -4 ⇒ y = 3 (Integer)

Put x = -5 y = 22/9 (Not an integer)

Put x = -13 ⇒ y = 8 (Integer)

Put x = -22 ⇒ y = 13 (Integer)

So here we can observe that values of x (starting with -1) with gap of 9 are giving the integer values for y.

So basically, we need to find the all the multiples of 9 between -500 and 500.

AP will be: -495, -486, …, 486, 495.

Number of terms = /9 + 1 = 110 + 1 = 111

∴ 111 integral values of x and y will satisfy the equation 5x + 9y = 7.

Bissoy MCQ

Related Questions

The following table shows the income (in rupees) for a particular month, together with their source, in respect of 5 employees (A, B, C, D and E).   A B C D E Salary 52,000 48,500 42,000 31,000 25,000 Overtime 0 0 1,500 2,500 3,200 Arrears 5.500 4,500 4,000 3,000 1,500 Bonus 3,500 3,000 2,500 2,000 2,000 Miscellaneous income 5,000 3,000 1,500 1,500 0 Total 66,000 59,000 40,000 40,000 31,700   For employee D, the income from overtime is what percentage of his total income?
The following table shows the income (In Rs.) for a particular month, together with their source, with respect to 5 employees (A, B, C, D, and E)   A B C D E Salary 52,000 48,500 42,000 31,000 25,000 Overtime 0 0 1,500 2,500 3,200 Arrears 5,500 4,500 4,000 3,000 1,500 Bonus 3,500 3,000 2,500 2,000 2,000 Miscellaneous income 5,000 3,000 2,000 1,500 0 Total 66,000 59,000 52,000 40,000 31,700   How many employees got more than a total of Rs. 10,000 as income other than salary?
The following table shows the income (in rupees) for a particular month, together with their source, in respect of 5 employees (A, B, C, D and E)   A B C D E Salary 52,000 48,500 42,000 31,000 25,000 Overtime 0 0 1,500 2,500 3,200 Arrears 5,500 4,500 4,000 3,000 1,500 Bonus 3,500 3,000 2,500 2,000 2,000 Miscellaneous income 5,000 3,000 2,000 1,500 0 Total 66,000 59,000 52,000 40,000 31,700 How many employees got more arrears than the average arrears received by all the employees?
The table below shows income (in rupees) for a particular month, together with their sources in respect of 5 employees A, B, C, D and E Employee A B C D E Salary 52,000 48,500 42,000 31,000 25,000 Overtime 0 0 1,500 2,500 3,200 Arrears 5,500 4,500 4,000 3,000 1,500 Bonus 3,500 3,000 2,500 2,000 2,000 Miscellaneous income 5,000 3,000 2,000 1,500 0 Total 66,000 59,000 52,000 40,000 31,700 How many employees have their salary more than four times their other incomes?
Which of the following explain the concept of values? (A) Values are beliefs tied inextricably to human emotion and behaviour (B) Values refer to desirable goals people strive to attain (C) Values are conflict-free (D) Values are ordered by importance relative to one another (E) Values are utilized primarily to effect change in knowledge of a person Choose the correct answer from the options given below :
With respect to the numerical evaluation of the definite integral $${\text{K}} = \int_{\text{a}}^{\text{b}} {{{\text{x}}^2}{\text{dx,}}} $$   where a and b are given, which of the following statements is/are TRUE?
I. The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral.
II. The value of K obtained using the Simpson's rule is always equal to the exact value of the definite integral.
A class III mathematics teacher gave the following questions to her students:  \(\begin{equation} \frac{ \begin{array}[b]{r} 256 \\ + 173 \end{array} }{ } \end{equation}\) \(\begin{equation} \frac{ \begin{array}[b]{r} 28 \\ + 32 \end{array} }{ } \end{equation}\) \(\begin{equation} \frac{ \begin{array}[b]{r} 129 \\ + 76 \end{array} }{ } \end{equation}\) Later she asks the students to solve a worksheet that has similar questions. Which of the following statements is appropriate for the given situation?
Which of the following statements are correct with the origin and development of values?
1. Values originate from human desires and interests.
2. Interaction between individuals in environment and situations originate values.
3. It is human being who originates values and protects it.
4. Attitude of an individual is based on values.
How many of integral value of x and y satisfy the equation 3y + 2x = 10, where x ≥ 0 and y ≥ 0?
What is the sum of all the integral values of ‘x’ that satisfy the inequality 0 < x (x + 1) (x + 3) (x + 4) < 210.