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` = 19Question: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 ..