Question:Factorise a `(x+1)^2` + (x+1)
Answer
a `(x+1)^2` + (x+1) =(x+1) {a(x+1) + 1} =(x+1) (ax+a+1)
Question:Factorise a `(x+1)^2` + (x+1)
a `(x+1)^2` + (x+1) =(x+1) {a(x+1) + 1} =(x+1) (ax+a+1)
Question:Solve the equations `3x + 4y = 5`.......................................... (i) `2x + 6y = 5` ...........................................(ii)
From (i), 3x = 5 - 4y x = `(5 - 4y)/ 3`. From (ii), 2x = 5 - 6y x = `(5 - 6y)/2` . `:. (5 - 4y)/3` = `(5 - 6y)/2` . Multiply throughout by 6 : 10 - 8y = 15 - 18y. `:.` 18y - 8y = 15 - 10. `:.` 10y = 5 and y = `1/2`. Substitute this value of y in x = `(5 - 6y)/2`. x = `(5 - 3)/2`= `2/2`= 1. The solution is x = 1; y =`1/2`.
Question:Solve the equations 7x + 3y = 9. . . . . . . . . . . . . . . . . . .(1) 11x - 5y =19. . . . . . . . . . . . . . . . . . .(2)
Eliminate y from the questions. Multiply (1) by 5: 35x + 15y=45 Multiply (2) by 3: 33x - 15y=57 add: 68x =102 `:.` x = `102/68` =`51/34` =`3/2` =1`1/2` substitute x = 1`1/2` in the equation 7x + 3y = 9 7(1`1/2`) + 3y = 9 `:.` 10`1/2` + 3y = 9 `:.` 3y = 9 - 10`1/2` = - 1`1/2` `:.` y = -`1/2` Check. when x = 1`1/2` and y = - `1/2` 7x + 3y =7(1`1/2`) + 3(-`1/2`) = 10`1/2` - 1`1/2` = 9. 11x - 5y = 11(1`1/2`) - 5(-`1/2`)=16`1/2`+2`1/2` = 19
Question:The perimeter of a rectangle is 44 m . The length is 2 m greater than the width. Find the length and width of the rectangle..
The perimeter of the rectangle is x 2(x+y) meters. `:.` 2(x+y) =44. Divide both sides of this equations by 2; x+y = 22. . . . . . . . . . . . . . . . . . . . .(1) We are also told that the length is 2 m greater than the width. `:.` x = y+2, x - y = 2 . . . . . . . . . . . . . . . . . . . .(2) we have the two equations x + y = 22 . . . . . . . . . . . . .(1) x - y = 2 . . . . . . . . . . . . . (2) add: 2x = 24. `:.` x = 12. Substitute in (1) : 12 + y = 22 `:.` y = 10. The length of the rectangle is 12 m ; its width is 10 m.
Question:The cost of 5 oranges and 4 lemons is 23 new pence.The cost of 3 oranges and 5 is 19 new pence.find the cost of an orange..
The cost of 5 oranges and 4 lemons is (5x + 4y) new pence. The cost of 3 oranges and 5 lemons is (3x + 5y) new pence. `:. 5x + 4y =23 . . . . . . . . . . . . . . . . . . .(1) 3x + 5y =19 . . . . . . . . . . . . . . . . . . .(2)` Multiply (1) by 3 : 15x + 12y = 69 Multiply (2) by 5 : 15x + 25y = 95 Subtract : - 13y = - 26 `:.` y = 2 substitute in (1) 5x + 8 = 23 `:.`5x =23 - 8 = 15 `:.` x = 3. The cost of an orange is 3 new pence ; the cost of a lemon is 2 new pence ..