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

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

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

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.

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.

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.

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

Your missing some operators in your equations.

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

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).