Basic algebra assistance please?

luke

I've been ill for most of the school year and I'm working to catch up.

I completely understand simultaneous equations but this makes no sense to me. Can someone give me a step by step solution please! it will be much appreciated!

Solve these simultaneous equations:

xy=4

1/2x-y=1

ian-h

You probably meant (1/2)x – y = 1 and xy = 4. If so, substitute y

(1/2)x – 4/x = 1, now multiply through by 2x and rearrange

x^2 – 2x – 8 = (x + 2)(x – 4) = 0

x = -2 with y = -2 or,

x = 4 and y = 1

But if you really meant 1/(2x) – y = 1 and xy = 4

y/8 - y = -(7/8)y = 1

y = -8/7

x = 4/y = 4/(-8/7) = -7/2

Regards – Ian H

may

Assuming you equations are x*y = 4, and one half of x minus y is 1...

If xy equals 4, then x equals 4/y.

Then, you plug that into the next equation. 1/2 (4/y) - y = 1.

If you simplify, you will get 4/2y - y = 1, and then 2/y - y = 1.

You multiply both sides by y, and you get 2- ysquared = y.

If you rearrange the equation, you'll get ysquared + y - 2 = 0.

Factor, and you end up with (y+2) (y-1). Your final answers will be -2 and 1 for y.

For x, since 4/y equals x, then 4/-2 is x, which is -2. Since y is also 1, then x is also 4.

So your answers would be:

x: -2, 4

y: -2, 1

sonia-simpson_60b8422ad4cbf

xy=4.............[1]

(1/2)x-y=1......[2]

Rewrite [2] solving for y

.....½x-y=1......[2]

.....y = ½x - 1..[2a]

Now substitute for y from [2a] into [1] and simplify

.....xy=4 .............[1]

.....x[½x - 1] = 4

.....½ x² - x = 4

.....½ x² - x - 4 = 0

Finally, solve for x using the quadratic formula

...........-(-1)±√((-1)²-4(½)(-4))

.....x = -----------------------------

...................2(½)

...........1±√(1+8)

.....x = -------------

...............1

.....x = 1±√9

.....x = 1±3

.....x = -2, 4........[3]

Go back and substitute x from [3] into either [1] or [2] or [2a] and solve for y. We'll use [2a]

.....When x = -2, y = ½(-2) - 1 = -2

.....When x = 4, y = ½(4) - 1 = 1

Your solutions are (x,y) = (-2,-2) and (x,y) = (4,1)......ANS

CHECK YOUR ANSWERS:

For (x,y)=(-2,-2)

.....xy = (-2)(-2) = 4..................CORRECT

.....(1/2)(-2) - (-2) = -1+2 = 1......CORRECT

For (x,y)=(4,1)

.....xy = (4)(1) = 4..................CORRECT

.....(1/2)(4) - (1) = 2-1 = 1........CORRECT

michelle

Luke, you have to learn how to use parenthesis" is it (1/2)x -y? (1/2x)-y? 1/(2x-y)? You should have learned this years ago.

nikki-russell_60b8422c4a1b1

It's not clear

(1/2)x-y ?

1/(2x-y)?

1/(2x)-y?

luke

Funny that Im unfortunate with disease, so I really am trying my best, condescending comments dont help.