Solve dy/dx=e^3x+2y by separation of variables

First, we will find y in terms of x. We will use the first equation to determine this.
4x+2y=2
We can subtract 4x from both sides:
2y=2-4x
And then divide both sides of the equation by two:
y=1-2x
Since we now have y in terms of x, we can substitute this into our second equation.
-3x-y=-3
-3x-(1-2x)=-3
Then, we can distribute the minus sign
-3x-1+2x=-3
-x-1=-3
Next, we can add 1 to both sides of the equation.


-x=-2
Finally, we divide both sides by negative one to isolate x.
x=2
Now that we have x's value, we can find y's value.
The first thing that we determined is:
y=1-2x
We can substitute in the value of x to this equation.
y=1-2x

y=1-4
y=-3
Therefore, we now have the values of both variables.
x=2
y=-3

x + 2y = -1

Do you really need a calculator to solve a linear equation?
Let us see how to solve it without a calculator.
Remove the parentheses fronm the second term on the left : y-3
Use the distributive property on the last term on the right side -2y-6
Take the term -3 to the right side, changing its sign in the process (becomes +3)
Take the -2y term to the left making it +2y.
3y +2y=18+3-6 or 5y=15 and the answer is straightforward .

As to your Casio FX300ES, it cannot solve equations because it does not have an EQUATION calculation mode. The Casios FX-115ES and FX-991ES have an Equation Mode. If you use any of the two to solve an equation in one variable (linear, quadratic or other) the unknown is taken to be x by default. You would have to change the name of the variable from y to x.

You have to put the equations into matrix form first. To do this, each variable has one column in the first matrix and you fill in the co-efficients for the variables. The second matrix has one column and contains all the numbers.

{ 2 -1 1 -1} = Matrix A
{ 1 3 -2 0}
{ 3 -2 0 4}
{-1 -3 -3 -1}

{-1} = Matrix B
{-5}
{ 1}
{-6}

{x=-2} = A*(B^-1)
{y=-.2}
{z=3}
{w=1/6}

I used excel for all my calculation and a helpful tutorial can be found here. I hope this helps and have a nice day!

(2x - 3y)(3x + 2y) = 2x*3x + 2x*2y - 3y*3x - 3y*2y
= 6x^2 + 4xy - 9xy - 6y^2
= 6x^2 - 5xy - 6y^2 You multiply each element in the first set of brackets by each element in the second set of brackets and then consolidate like terms and arrange them in sequence of powers, first x and then y. So:
2x by 3x = 6x squared
2x by 2y = 4xy
-3y by 3x = -9xy
-3y by 2y = 6y squared

6x squared -5xy + 6y squared

And your question is? If you just want to know how to solve this system, you only need to substitute one equation into the other and solve for the remaining unknown.

y=3x (equation 2), so plug it into equation 1

7x-2y=1
7x-2(3x)=1
7x-6x=1
x=1

from equation 2 then, you know y=3x=3

3x(3x)/2y+(3x) - 3x-2y/3x+2y

Hi joanmae jmeh;

You can add these equations just like you would numbers

3x + 2y = 7
5x - 2y = 1
-----------------------
8x =8
x=1
Now plug x = 1 back into either equation and you can solve for y
Y = 2

When you add the 2 equations together the +2y and the -2y cancel
out

Hope this helps Loringh Please leave a rating for me Thks

(x+3y=0)*3=3x+9y
y=1 x= -3

B. 2((2-Y)/3)-Y=3
2(2-Y)-Y=9
4-2Y-Y=9
-3Y=9-4
-3Y=5
-Y=5/3
Y=-1.67

A. 3X+(-1.67)=2
3X-1.67=2
3X=2+1.67
3X=3.67
X=3.67/3
X=1.22