 Hello and welcome to the session. Let us understand the following question today. Solve the following pair of linear question by substitution and cross-multiplication method. Given to us is 8x plus piy is equal to 9, 3x plus 2y is equal to 4. Now that is why this equation. Given equations are 8x plus piy is equal to 9 and 3x plus 2y is equal to 4. Now first solving it by substitution method. Let us learn this equation as 1 and this as 2. Now from equation 2 we get we have 3x plus 2y is equal to 4. This implies 3x is equal to 4 minus 2y. This implies x is equal to 4 minus 2y by 3. Let us name it as equation 3. Now substituting the value of x from 3 into 1. Now we will put this value of x in our equation 1. So we have our equation 1 as 8x plus piy is equal to 9. Now which implies 8 multiplied by 4 minus 2y by 3 plus piy is equal to 9. Now solving this for y which implies 32 minus 16y by 3 plus piy is equal to 9. Now multiplying both sides by 3 so we get 3 multiplied by 32 minus 16y by 3 plus 3 multiplied by 5y is equal to 9 multiplied by 3. This 3 and 3 gets cancelled which implies 32 minus 16y plus 15y is equal to 27. Which implies minus 5 is equal to 27 minus 32 which implies minus y is equal to minus 5. Now this minus and minus gets cancelled so we get y is equal to 5. Now substituting y is equal to 5 in equation 3. So we get we have x is equal to 4 minus 2y by 3 as our equation 3. So putting the value of y which is equal to 4 minus 2 into 5 by 3 which is equal to 4 minus 10 by 3 which is equal to minus 6 by 3. Now this gets cancelled y minus 2 so it implies x is equal to minus 2. Hence x is equal to minus 2 and y is equal to 5. I hope you understood the question for substitution so now solving it for by cross multiplication. Now comparing the given equations with a1x plus b1y plus c1 is equal to 0 and a2x plus b2y plus c2 is equal to 0. So we get a1 is equal to 8, a2 is equal to 3, b1 is equal to 5, b2 is equal to 2, c1 is equal to minus 9 and c2 is equal to minus 4. Then using the formula for cross multiplication that is x upon b1 c2 minus b2 c1 which is equal to y upon c1 a2 minus c2 a1 which is equal to 1 upon a1 b2 minus a2 b1. Now substituting the values for a1 b1 c1 and a2 b2 and c2 so we get it implies x upon 5 into minus 4 minus 2 into minus 9 which is equal to y upon minus 9 into 3 minus minus 4 into 8 which is equal to 1 upon 8 into 2 minus 3 into 5. Which implies x upon minus 20 plus 18 is equal to y upon minus 27 plus 32 which is equal to 1 upon 16 minus 15 which implies xy minus 2 is equal to y by 5 is equal to 1 by 1. Therefore xy minus 2 equal to 1 and y by 5 is equal to 1 which implies x is equal to minus 2 and this implies y is equal to 5. Hence x is equal to minus 2 and y is equal to 5. Therefore x is equal to minus 2 and y is equal to 5 is a solution of a given equation by both the method the substitution and cross multiplication. So this is our required answer. I hope you understood the question. Bye and have a nice day.