(2x+3y)(3x+2y) - Yahoo Computers & Internet

Two equations:
x = first number
y = second number
2x - y = -1
y = 1 + 2x
2y + 3x = 9
2(1 + 2x) + 3x = 9
2 + 7x = 9
7x = 7
x = 1
y = 2(1) + 1 = 3

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

To find the solution, first find the value of y for each equation.
Then substitue one equation into the other so that you only the x variable left.
Then just solve for x.
Once you have a value for x, then you can easily solve for y.


So for the first equation:

3y - 6x = -3
3y = 6x - 3

y = 2x - 1


Now for the second equation:

2y + 8x = 10
2y = -8x + 10

y = -4x + 5

Since both equations equal y, they also equal each other, therefore:

2x - 1 = -4x + 5

Now just solve for x:

2x + 4x = 5 + 1
6x = 6

x=1

Now substitute x=1 into either original equation:

y = 2x - 1
y = 2 (1) - 1
y = 2 - 1

y = 1


Therefore the solution is x=1 and y=1



Good luck, I hope that helps.


Joe.

Price of bag of chips s X and price of box of pretzels is Y.
Now you can write following equations:

2X+3Y=413
X+2Y=239

From second equation you know that X is 239-2Y, and you put that in first equation:

2*(239-2Y)+3Y=413

or

-4Y+3Y=413-2*239

Finally we have for Y: Y=65 and X=239-2Y=109.

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!

2y - x = 3
x = 3y - 5

Add the two equations side by side,

2y - x + x = 3 + 3y - 5

2y = 3y - 2

y = 2

Plug this in the second equation to get x,

x = 3(2) - 5

x = 1

So the solution is x = 1, y = 2

or in ordered pair notation (1, 2)

Consider the following system of 3 equations in 3 unknowns:
x + y = 2
2x + 3y + z = 4
x + 2y + 2z = 6Our goal is to transform this system into an equivalent system from which it is easy to find the solutions. We now do this step by step.

• Subtract 2*(Row1) from Row2 and place the result in the second row; subtract Row1 from Row2 and place in the third row. Leave Row1 as is.

x + y = 2
y + z = 0
y + 2z = 4

• Subtract Row2 from Row3, and place the result in row3. Leave Row1 and Row2 as they are.

x + y = 2
y + z = 0
z = 4 From the last form of the system we can deduce the following unique solution to the system:

z = 4, y = -4, and x = 2-(-4) = 6Equivalently, we say that the unique solution to this system is (x, y, z) = (6, -4, 4).

(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