Question

If we have a pair of linear equations as 29x + 37y = 103, 37x + 29y = 95, then
(A). x = 1, y =2
(B). x = 2, y = 1
(C). x = 2, y = 3
(D). x = 3, y = 2

Answer 1

Hint: Consider the given two equations multiply the \[{{1}^{st}}\] equation by 37 and \[{{2}^{nd}}\] equation by 29 and subtract each other to solve the values of x and y for which the equation satisfies.

Complete step-by-step solution -
In the question, we are given that the two equations are 29x + 37y = 103 and 37x + 29y = 95 and we have to find the values of x and y for which the two equations satisfy.
For solving the two equations we will use the method of elimination which is done in some steps as mentioned below:
(i). At first, finding the two equations that have the same variable. Then we have to multiply each equation by a number such that their coefficients are the same.
(ii). After doing the above process we will subtract the two new formed equations.
(iii). We will repeat until we are left with a single variable, after that we will solve for it.
(iv). After finding the value of the solved variable will substitute back into the original equation to find another value too.
The given equations are let they be named as: -
29x + 37y = 103 ----- (i)
37x + 29y = 95 ------ (ii)
After this first multiply the equation (i) by 37 and the equation (ii) by 29 so after multiplication we get,
1073x + 1369y = 3811
1073x + 841y = 2755
Now subtracting both of the equation we get,
528y = 1056
So, the value of y is 2.
Now we will substitute the value of y as 2 in equation (i) we get,
\[29x+37\times 2=103\]
Or, 29x + 74 = 103
Hence the value of 19x = 29 or the value of x is 1.
Hence the value of x and y is 1 and 2 respectively.
So, the correct option is (a).

Note: There is a method to check if the answer is correct or not we can check that the value of x and y are right or wrong by substituting it in the given equations of the problem. If they satisfy the answer, got is right.