 Hello friends, so welcome to this session of problem solving in linear equation in two variables So here we have taken a word problem, and we are going to solve this problem Now this problem is related to numbers. So first of all, we would like to understand how numbers are represented in decimal system So let us say we have a number 15. So 15 is equal to nothing but 10 into the 10th place digit that is 1 if you see the 10th place digit here is 1 and unit's place is 5. This is 10th place and This one is unit's place Isn't it? So the number value is nothing but 10 into 1 that is the unit's place digit plus 5 Okay, now many questions will be there where the numbers will be reversed So if you see if I the digits are reversed So if you see here if we reverse the digits, you will get 51 and 51 is nothing but 5 into 10 again units 10th place digit into 10 plus unit's place digit that is 1 right So this one here is 10th place and this one 1 is unit's place So this is what? Our Decimal number 2 digit number is represented as okay. Now what does the question say? In this question our 2 digit Number is 3. So if you will be looking for these markers is means equation, right? So let us write this is first So the direct translation of is into mathematics is equal to now a 2 digit number is so that means on the left hand side There is a 2 digit number. So let us say let us say we will say that let the digits Let the digits be x and y so the 2 digit number will be nothing but 10 x plus y Now this is equal to 3 more than more than means added to so 3 and more than is translated as plus 4 times so 4 Times is into the sum of digits sum of digits will be x plus Why this is how I translated our English statement into a mathematical equation, okay? So now simplify this you will get 10 x plus y equals 3 plus 4 x plus 4 y so if you simplify further you'll get 6 x minus 3 y equals 3 This implies 2 x minus y is equal to 1 Dividing the entire equation by 3. So this is let us say equation number one Now let us go to the second statement If 18 is added to so let us add 18 add means plus added to what to the number? What was the number 10 x plus y? The digits are reverse. So if you reverse the digit, what will you get? What new number will be 10 times y plus x? Isn't it so here you get the second equation simplify again you'll get 9 y minus 9 x is equal to 18 or y minus x equals 2 This is equation number 2 now you add now the case is simply left to solve these two equations So add 1 plus 2 why am I adding because I can see a minus y here and a plus by here if I add LHS My y will get eliminated. So 2 x minus x is equal to 1 plus 2. So x is equal to 3 Now if x is 3, what is y? So y is nothing but 2 plus x I'm equation 2 so 2 plus x is 2 plus 3 that is 5 Hence my number was x y that is what was the number initial number will be 35 is the original number Original number let us check whether it is correct or not. So let us see the condition. So first is you Number was equal should be equal to what? 3 plus 4 times some of the digits. So 3 plus 5, which is true both are 35 And the second condition was if 18 is added to the number the number digits reverse Yes, it does it is our reverse. So hence our solution that the number original number is 35 is correct Okay, so always remember what is the learning learning is? learning is Wherever you see is or you have to say equal to so this means equal to right more than added to Added to if these terms are there then you have to write plus right times means multiplication, okay difference of Is negative that is Right, and then to digit numbers also be learned How are numbers placed so numbers are if there are two if there is a two digit number two digit number Two digit number then the number value of the number value of the number is equal to 10 times 10th place digit 10th place digit Plus This is how a number in decimal system Represented hope you understood the process. Thank you