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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!

Posted on May 05, 2011

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y = x+1

y = (4) + 1

y = 5

y = x + 1

y = (-4) + 1

y = -3

2y - 2 = 2x

2y - 2 = 2 (4)

2y - 2 = 8

2y - 2 + 2 = 8 + 2

2y = 10

2y/2 = 10/2

y = 5

2y - 2 = 2(-4)

2y - 2 = -8

2y -2 + 2 = -8 + 2

2y = -6

2y / 2 = -6 /2

y = -3

The results are the same, implying that they are the same line.

Why?

2y - 2 = 2x

2y - 2 + 2 = 2x + 2

2y = 2x + 2

divide everything by 2

y = x + 1

Good luck,

Paul

y = (4) + 1

y = 5

y = x + 1

y = (-4) + 1

y = -3

2y - 2 = 2x

2y - 2 = 2 (4)

2y - 2 = 8

2y - 2 + 2 = 8 + 2

2y = 10

2y/2 = 10/2

y = 5

2y - 2 = 2(-4)

2y - 2 = -8

2y -2 + 2 = -8 + 2

2y = -6

2y / 2 = -6 /2

y = -3

The results are the same, implying that they are the same line.

Why?

2y - 2 = 2x

2y - 2 + 2 = 2x + 2

2y = 2x + 2

divide everything by 2

y = x + 1

Good luck,

Paul

Feb 07, 2017 | The Office Equipment & Supplies

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

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

Jan 13, 2015 | SoftMath Algebrator - Algebra Homework...

This is no linear system. You cannot solve it like that using the matrix techniques. Haven't you made a mistake in writing the equations?

If that is tryly the system you want to solve, I suggest that you make a change of variables as follows:

X=1/x , Y= 1/y, Z=1/z (it being understood that x, y, z cannot be equal to 0). You will have to exclude the values x=0, y=0, z=0

Not I am not being sloppy, X and x are different entities, same with Y and y, Z and z.

Your system becomes

**2X+3Y-1Z=26**

1X+3Y-2Z=36

2X+4Y-5Z=52

Now that is a linear system. Solve it using matrices or Cramer's rule, When you obtain X, Y, and Z, get x=1/X, y=1/y, z=1/Z

The actual implementation of the solution method will depend on the exact model of calculator you are using. Not knowing that, I cannot advise you how to do it.

If I have not made any mistakes, the results are X=-58/9,Y=106/9, Z=-32/9. And x, y, z are just the reciprocals of their namesake.

If that is tryly the system you want to solve, I suggest that you make a change of variables as follows:

X=1/x , Y= 1/y, Z=1/z (it being understood that x, y, z cannot be equal to 0). You will have to exclude the values x=0, y=0, z=0

Not I am not being sloppy, X and x are different entities, same with Y and y, Z and z.

Your system becomes

1X+3Y-2Z=36

2X+4Y-5Z=52

Now that is a linear system. Solve it using matrices or Cramer's rule, When you obtain X, Y, and Z, get x=1/X, y=1/y, z=1/Z

The actual implementation of the solution method will depend on the exact model of calculator you are using. Not knowing that, I cannot advise you how to do it.

If I have not made any mistakes, the results are X=-58/9,Y=106/9, Z=-32/9. And x, y, z are just the reciprocals of their namesake.

Dec 13, 2013 | Office Equipment & Supplies

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.

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

Now for the second equation:

2y + 8x = 10

2y = -8x + 10

2x - 1 = -4x + 5

Now just solve for x:

2x + 4x = 5 + 1

6x = 6

y = 2x - 1

y = 2 (1) - 1

y = 2 - 1

Good luck, I hope that helps.

Joe.

Nov 09, 2011 | Texas Instruments TI-84 Plus Silver...

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.

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.

Sep 08, 2011 | Casio fx-300ES Calculator

This should start wit X=something and Y=something, sorry I'm not an human algebra calculator....

Jul 29, 2011 | Computers & Internet

Your missing some operators in your equations.

Aug 07, 2010 | Matrix 226R (VPR226R) PC Desktop

6x+6=4x+12

Since 4x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 4x from both sides.

6x+6-4x=12

Since 6x and -4x are like terms, add -4x to 6x to get 2x.

2x+6=12

Since 6 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 6 from both sides.

2x=-6+12

Add 12 to -6 to get 6.

2x=6

Divide each term in the equation by 2.

(2x)/(2)=(6)/(2)

Simplify the left-hand side of the equation by canceling the common factors.

x=(6)/(2)

Simplify the right-hand side of the equation by simplifying each term.

x=3

Good Luck

Since 4x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 4x from both sides.

6x+6-4x=12

Since 6x and -4x are like terms, add -4x to 6x to get 2x.

2x+6=12

Since 6 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 6 from both sides.

2x=-6+12

Add 12 to -6 to get 6.

2x=6

Divide each term in the equation by 2.

(2x)/(2)=(6)/(2)

Simplify the left-hand side of the equation by canceling the common factors.

x=(6)/(2)

Simplify the right-hand side of the equation by simplifying each term.

x=3

Good Luck

Sep 10, 2009 | Audio Players & Recorders

Consider the following system of **3 equations in 3 unknowns**:

*x + y = *2

**2***x + *3*y + z = *4

*x + *2*y + *2*z = *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.
* x + y = *2

* y + z = *0

* y + *2*z = *4
*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).

- 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.

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

Sep 17, 2008 | Belkin (F5D7230-4) Router (587009)

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