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2x -y +z -w = -1 x +3y -2z = -5 3x -2y +4w = 1 -x +y -3z -w = -6 solve for the variables w,x,y,z using matrix equation

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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
{ 1}

{x=-2} = A*(B^-1)

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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Substitute 4 and -4 for x in the equations y=x+1 and 2y-2=2x. Describe the results

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.


2y - 2 = 2x
2y - 2 + 2 = 2x + 2
2y = 2x + 2
divide everything by 2
y = x + 1

Good luck,


Feb 07, 2017 | The Office Equipment & Supplies

1 Answer

How do I solve (3x-2y)2(3xy-3)

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

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

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

1 Answer

Problems matrix

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

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

1 Answer

What ia the sulution of 3y-6x=-3

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


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.


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

1 Answer

How do I solve for y, 2y + (y-3)=18 - 2 (y+3). with the casio fx-300es? and if I cant whats the calculator that will. thanx

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.

Sep 08, 2011 | Casio fx-300ES Calculator

2 Answers

2x - 4y = 20 4x + 2y = -20

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

Jul 29, 2011 | Computers & Internet

1 Answer

Test for conistency and solve the system 2x y

Your missing some operators in your equations.

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

3 Answers

Find the value of the variable ''x'' 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.
Since 6x and -4x are like terms, add -4x to 6x to get 2x.
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.
Add 12 to -6 to get 6.
Divide each term in the equation by 2.
Simplify the left-hand side of the equation by canceling the common factors.
Simplify the right-hand side of the equation by simplifying each term.

Good Luck

Sep 10, 2009 | Audio Players & Recorders

2 Answers

Algebra college

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).

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

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