Solve the following equation 4cos^4x-1=0

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Posted on Jan 02, 2017

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...

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...

You only presenting one side of the equation with what you got to get:
(x-1)(x-4) = x^2-x-4x+4
you get that by multiplying the factors in the brackets with each other to expand the equation without the other side of the equation you can't solve for x

Nov 26, 2010 | Computers & Internet

You cannot solve this equation,at least not in the regular meaning of solving which is to find the roots. This is a relation linking two variables x and y, in other words a function. There are an infinite number of orderd pairs tha satisfy this equation.

You can draw it as y=1/5(-4x 12) but your calculator cannot graph.

If you want to use the Solve( command on this calculator you must supply the value of y.

You can draw it as y=1/5(-4x 12) but your calculator cannot graph.

If you want to use the Solve( command on this calculator you must supply the value of y.

Sep 23, 2010 | Casio FX-115ES Scientific Calculator

The easiest solution would be to move the variable to only one side. This is not that difficult. For example your given equation is 8(3x-5)-4=4x-10; subtracting both sides of this equation by 4x would give 8(3x-5)-4-4x=10.

Jun 28, 2010 | Texas Instruments TI-82 Calculator

4x+7=11 Solve for "x".

subtract 7 from each side of the equation

4x +7(-7)=11(-7) = 4x=4

divide both sides of the equation by 4

4x/4=4/4

therefore

x=1

Correct?

subtract 7 from each side of the equation

4x +7(-7)=11(-7) = 4x=4

divide both sides of the equation by 4

4x/4=4/4

therefore

x=1

Correct?

Dec 06, 2009 | 2006 Harley Davidson FXDI35 35th...

Hello,

I am not lecturing you but I would rather you understand how to do the manipulations involved in isolating a variable.

You want to isolate y, Ok

Start stripping it of all that is not y.

3y + 4x =6. (Addition is commutative, I can change the order of addition)

The term with y is** added **to 4x. If I want the term in y alone on one side I perform the** inverse operation of addition**, a **substraction**. I subtract 4x from both sides.

3y+4x-4x=6-4x. But 4x-4x=0, and we are left with

**3y= - 4x+6**

This operation is sometimes summarized as make one term change side while changing its sign

It would do no harm to put the right side of the foregoing equation in parentheses. I do that to avoid errors)

3y= (-4x+6).

Now y is**multiplied** by the number 3. To isolate y I have to perform the **inverse operation** of the multiplication, namely the division by 3

3y/3 =(-4x+6)/3. The left hand side is just y

**y= (-4x+6)/3.**

While result is correct, I can also open the parentheses

y= -4x/3 +6/3

**y= -(4/3)*x +2.**

Hope it helps.

I am not lecturing you but I would rather you understand how to do the manipulations involved in isolating a variable.

You want to isolate y, Ok

Start stripping it of all that is not y.

3y + 4x =6. (Addition is commutative, I can change the order of addition)

The term with y is

3y+4x-4x=6-4x. But 4x-4x=0, and we are left with

This operation is sometimes summarized as make one term change side while changing its sign

It would do no harm to put the right side of the foregoing equation in parentheses. I do that to avoid errors)

3y= (-4x+6).

Now y is

3y/3 =(-4x+6)/3. The left hand side is just y

While result is correct, I can also open the parentheses

y= -4x/3 +6/3

Hope it helps.

Oct 22, 2009 | Texas Instruments TI-89 Calculator

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

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

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

Dec 01, 2008 | Bagatrix Algebra Solved! 2005 (105101) for...

Just plug in one side of the equation and find the answer. Then plug in the other side and compare answers.

Feb 19, 2008 | Texas Instruments TI-89 Calculator

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