Please help! algebra problems?

Question

. if 4r+7s=23 and r-2s=17, then 3r+3s=?

a) 8 b) 24 c)32 d) 40 e) 48

i got 6 for this problem, but its not correct.

2. if xy/x+y=1 and x does not equal to -y, what is x in terms of y?

3.if h=x^2-1/x+1 + x^2-1/x-1, what is x in terms of h?

4.if wx=z, which of the following expressions is equal to xz?

a) w/z^2 b)w^2/z c)wz^2 d) w^2z e) z^2/w

Answer 1

1st one is 24. r = 11, s = -3

Answer 2

ok...here is number 1.

r=17+2s

4(17+2s)+7s=23

68+8s+7s=23

15s=-45

s=-3

r-2(-3)=17

r+6=17

r=11

3(11)+3(-3)=24

b)24

Answer 3

1) 4r + 7s = 23 and r - 2s = 17

the second equation becomes: r = 2s + 17

substitute this into the first equation:

4(2s + 17) + 7s = 23

8s + 68 + 7s = 23

15s = -45

s = -3

if s = -3 then r = 2(-3) + 17

r = -6 + 17

r = 11

therefore, 3r + 3s =

3(11) + 3(-3)

33 - 9

24

2) xy/(x+y) = 1

xy = x + y (because x is not equal to -y we can do this, otherwise the denominator is zero which can't happen)

xy - x = y

x(y - 1) = y

x = y/(y-1)

3) h = [(x^2 - 1)/(x + 1)] + (x^2 - 1)/(x - 1)

h = [(x+1)(x-1)/(x+1)] + [(x+1)(x-1)/(x-1)] using difference of squares to factor

h = (x-1) + (x + 1) after cancelling numerators and denominators

h = x + x - 1 + 1

h = 2x

h/2 = x

4) wx = z square both sides w^2(x^2) = z^2

need to turn each equation into just x's and z's

a) w/z^2

w/[w^2(x^2)]

1/w(x^2)

1/[(z/x)(x^2)] substitute that w = z/x

1/[zx] therefore, doesn't equal xz

b) w^2/z

[(z^2/x^2)/z

z/x^2 therefore, doesn't equal xz

c) wz^2

(z/x)z^2

z^3/x therefore doesn't equal xz

d) w^2z

(z^2/x^2)z

z^3/x^2 therefore doesn't equal xz

e) z^2/w

z^2/(z/x)

z^2x/z

zx therefore DOES equal xz