1. ## solving these sorry

just seen a post underneath nearly the same, maybe were doing the same course :P but anyway im having real trouble with these and if anyone could help it would be great ( oh and i dont know how to write squared and such so i copied it off that post too

a) x(2) + 3x + 5y = 20
x + 3y = 1

b) 2x + y = 8
4x(2) - 3y(2) = 1

c) x + 2y = 5
5x(2) + 4y(2) + 12x = 29

d) x(2) + y(2) + 4x + 6y - 40 = 0
x - y = 10

thank you
thank you
thank you

2. Hello, Kim!

I'll do the last one . . . it seems to be the messiest one.
I hope you can use my solution as a template for solving the others.

d) .[1] .x² + y² + 4x + 6y - 40 .= .0
. . .[2] .x - y .= .10

We have a quadratic equation and a linear equation.

Solve the linear equation for one of its variables.
. . From [2], we have: .y .= .x - 10 .[3]

Substitute into [1]:
. . . . .x² + (x - 10)² + 4x + 6(x - 10) - 40 .= .0
. .x² + x² - 20x + 100 + 4x + 6x - 60 - 40 .= .0
. . . . . . . . . . . . . . . . . . . . . . .2x² - 10x .= .0
Factor: . . . . . . . . . . . . . . . . . .2x(x - 5) .= .0

Solve the two equations:
. . . 2x .= .0 . . . x .= .0
. . x - 5 .= .0 . . x .= .5

Substitute into [3]:
. . x = 0: . y .= .0 - 10 . . y .= -10
. . x = 5: . y .= .5 - 10 . . y .= .-5

Therefore, the solutions are: .(0,-10) and (5,-5)

3. Originally Posted by Kim2425
a) x^2 + 3x + 5y = 20
x + 3y = 1
Since most people avoid fractions where ever they can I will solve the bottom equation for x. (Always solve the linear equation first, if there is one.)
x = 1 - 3y

Insert this value of x into the top equation:
(1 - 3y)^2 + 3(1 - 3y) + 5y = 20

(1 - 6y + 9y^2) +(3 - 9y) + 5y = 20

1 - 6y + 9y^2 + 3 - 9y + 5y = 20

9y^2 - 10y - 16 = 0

y = [-(-10) (+/-) sqrt{(-10)^2 - 4*9*(-16)}]/(2*9)

y = [10 (+/-) sqrt{100 + 576}]/18

y = [10 (+/-) sqrt{676}]/18

y = [10 (+/-) 26]/18

y = [10 + 26]/18 = 2
or
y = [10 - 26]/18 = -8/9

(Which means the quadratic factors. Ah well, the good ol' quadratic formula always works, at least! )

So anyway:
x = 1 - 3y

y = 2 ==> x = 1 - 3*2 = 1 - 6 = -5

y = -8/9 ==> x = 1 - 3*(-8/9) = 1 + 8/3 = 11/3

So the solutions are
(x, y) = (11/3, -8/9)
(x, y) = (-5, 2)

-Dan