How to Solve Simultaneous Equations with Multiplication Symbols?

[AstroBoy1]

Can someone solve this, i know its not very hard but for me it is :/
View attachment 2014
The dot . is meaned to be * (multiplication)

can someone help me :)

 

[Amer]

Can someone solve this, i know its not very hard but for me it is :/
View attachment 2014
The dot . is meaned to be * (multiplication)

can someone help me :)

You want to find $ \dfrac{x}{4} + \dfrac{x}{4} = \dfrac{x}{2} $ we want half of x

$ \dfrac{x+y}{4} = 1 - \dfrac{xy}{2} $

$ \dfrac{2(2xy)}{3} - \dfrac{3x-y}{4} = 3 $

From the first equation write y with respect to x, first i would like to multiply it with 4 to eliminate the denominator

$ x+y = 4 - 2xy \Rightarrow y( 1 + 2x) = 4-x \Rightarrow y = \dfrac{4 -x }{1+2x} $
Sub it in the second and solve it for x
Tell us what you get...
I supposed that (1+2x) =/= 0

 

[anemone]

Hey Astroboy,

I noticed the system of equations that you cited has no solution over the real numbers. Are you sure you have copied the problem correctly

 

[soroban]

Hello, AstroBoy!

I agree with anemone.

$$\begin{array}{cccc}\tfrac{1}{4}(x+y) \;=\;1 - \tfrac{1}{2}xy & [1] \\ \tfrac{2}{3}(2xy) - \tfrac{1}{4}(3x-y) \;=\;3 & [2] \end{array}$$

$$\begin{array}{cccccccc}4\times[1]& x+y \,=\,4-2xy \\ 12\times[2] & 16xy - 9x + 3y \,=\,36 \end{array}$$We have: .$$\begin{array}{cccc}x + y + 2xy &=& 4 & [3] \\ 9x - 3y - 16xy &=& \text{-}36 & [4] \end{array}$$
$$\begin{array}{cccccc}8\times[3] & 8x + 8y + 16xy &=& 32 \\ \text{Add [4]} & 9x - 3y - 16xy &=& \text{-}36 \end{array}$$

We have: .$$17x + 5y \:=\:\text{-}4 \quad\Rightarrow\quad y \:=\:\text{-}\frac{17x+4}{5}$$

Substitute into [3]: .$$x - \frac{17x+4}{5} + 2x\left(\text{-}\frac{17x+4}{5}\right) \:=\:4$$

Multiply by 5: .$$5x - 17x - 4 - 34x^2 - 8x \:=\:20$$

And we have: .$$34x^2 + 20x + 24 \:=\:0$$But .$$17x^2 + 10x + 12 \:=\:0$$ .has no real roots.

 

[CellCoree]

Hello,

I would be happy to assist you with solving simultaneous equations. Can you please provide the specific equations that you need help with? It will be easier for me to guide you through the process if I have the equations in front of me.

Also, just to clarify, when you mention the dot, do you mean the symbol for multiplication ( * )?

I am confident that with some guidance, you will be able to solve these equations successfully. Looking forward to your response.