Question

If we have two linear equations as 7x + 13y = 27 and 13x + 7y = 33, then find the value of x + y.

Answer 1

Hint:- We have to only multiply 7x + 13y = 27 by 13 and 13x + 7y = 33 by 7 and after that we subtract both of the equations to find the value of y and after that we put the value of y in any of the equation to find the value of x.

Complete step-by-step answer: -
As we know that we are given two linear equations and that were,
7x + 13y = 27 (1)
13x + 7y = 33 (2)
So, now we have to find the value of x and y using these two equations and then add them to find the value of x and y.
So, for solving equation 1 and equation 2.
So, multiplying equation 1 by 13 and multiplying equation 2 by 7. We get,
91x + 169y = 351 (1)
91x + 49y = 231 (2)
Now subtracting equation 1 and 2. We get,
120y = 120
Dividing both sides of the above equation by 120. We get,
y = 1
Now, putting the value of y in equation 1. We get,
7x + 13 = 27
Now subtracting both sides of the above equation by 13. We get,
7x = 14
Now dividing both sides of the above equation by 7. We get,
x = 2
Now we had to find the value of x + y.
So, x + y = 2 + 1 = 3
Hence, the value of x + y will be equal to 3.

Note:- Whenever we come up with this type of problem then there is also another method to find the value of x and y. We can also find the value of x and y by using the cross-multiplication method. First write the given equations in form of \[ax + by + c = 0\] and after that we can compare the given equations with \[{a_1}x + {b_1}y + {c_1} = 0\] and \[{a_2}x + {b_2}y + {c_2} = 0\]. And apply the direct formula to find the value of x and y using cross-multiplication method which is \[x = \dfrac{{\left( {{b_1}{c_2} - {b_2}{c_1}} \right)}}{{\left( {{a_1}{b_2} - {a_2}{b_1}} \right)}}\] and \[y = \dfrac{{\left( {{c_1}{a_2} - {c_2}{a_1}} \right)}}{{\left( {{a_1}{b_2} - {a_2}{b_1}} \right)}}\]. And after that we had to find the sum of x and y.