someone pls help! maths : solve simultaneous eq.?

Question

2x+2y=7
x²-4y²=8

Answer 1

We could start by solving the first equation for one of the variables, and then we'll substitute that expression into the other equation. (The "addition" or "elimination" method of solving simultaneous equations really doesn't work well when one of the equations is quadratic, like equation 2 is here.)

In fact, let's cheat a little: let's realize that (2y)² = 4y², and just solve Eq 1 for 2y:

2y = 7 - 2x

Then Eq 2 becomes:

x² - (7 - 2x)² = 8

Squaring the expression in parentheses gives:
x² - (49 - 28x + 4x²) = 8

Distributing the negative and combining like terms:
-3x² + 28x - 49 = 8

Subtracting 8 from both sides:
-3x² + 28x - 57 = 0

Multiplying both sides by -1:
3x² - 28x + 57 = 0

Now, is this factorable? Yes, like this:
(3x - 19)(x - 3) = 0

So, either x - 3 = 0 or 3x - 19 = 0. That means either x = 3 or x = 19/3.

We can find a y-value for each of those x-values by plugging x back into Eq 1. If x = 3, y = 1/2. If x = 19/3, y = -17/6.

All you need to do now is test both ordered pairs (3, 1/2) and (19/3, -17/6) in both equations to make sure they work. Good luck!

Answer 2

You have to solve the first equation for x then plug it into the second.

2x = 7 - 2y; x = (7-2y)/2

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

etc.

Unless they edit them the 3 answers above are wrong, check your work!

Answer 3

form the equation #1 you can find that x=7/2 - y so in the equation #2 we get (7/2 -y)^2 -4y^2=8 then solve it.
good luck

Answer 4

How about a hint?
The first equation gives x + y = 7/2, y = 7/2 -x.
Now plug this into the second equation and
solve via the quadratic formula.

Answer 5

x= 35/2
y=7/12

Answer 6

2x+2y=7
2y=7-2x
4y^2=(7-2x)^2
substituting in given eqn
x^2-4y^2=8
x^2-(7-2x)^2=8
x^2-49+28x-4x^2=8
3x^2-28x+57=0
3x^2-9x-19x=57=0
3x(x-3)-19(x-3)=0
(x-3)(3x-19)=0
x=3,19/3
from given eqution
2y=7-2x
y=7/2-x=7/2-x
y=1/2,53/26

Answer 7

Solve the first equation for x (or y).

Then substitute that into your second equation.

That will allow you to solve for y (or x).

Now return to the first equation using the answer you just found for y (or x) and solve for x (or y).

Answer 8

y=(7-2x)/2
put this in equation 2
x2-[4(7-2x)/2]2 =8
x2-(14-4x)2 =8
x2-196-16x2+112x = 8
15x2-112x+204 = 0

just solve it after this..

Answer 9

2x+2y=7
x^2-4y^2=8
x^2-(7-2x)^2=8
x^2-49-4x^2+28x-8=0
-3x^2+28x-57=0
=>3x^2-28x+57=0
x=[28+/-rt(784-684)]/3
x=[28+/-10]/3
=6 or 38/3

Answer 10

x=(7-2y)/2
(49-4y2)/4-4y2=8
49-4y2-16y2=32
20y2=17
y2=17/20