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Nov 07, 2015 | Toyota Cars & Trucks

x + y = 84

x = 4y + 9

so 4y + 9 +y = 84

5y = 75

y = 15

x = 60 + 9 = 69

Check

69 + 15 = 84

x = 4y + 9

so 4y + 9 +y = 84

5y = 75

y = 15

x = 60 + 9 = 69

Check

69 + 15 = 84

Apr 21, 2014 | Computers & Internet

Write the equality in the form y=(5X+3)/(4X-5). Insert parentheses to ensure a correct result.

- Multiply both sides of the equality by (4X-5). This gives (4X-5)y=(5X+3).
- Open the parentheses as 4Xy-5y=5X+3
- Subtract 5X from both sides 4Xy-5y-5X=5X-5X+3
- Add 5y to both sides 4Xy-5X-5y+5y=5y+3 or 4Xy-5X=5y+3
- Factor the X on the left side X(4y-5)=5y+3
- If 4y-5 does not vanish, you can isolate X by dividing both members of the equality by (4y-5).
- You get X=(5y+3)/(4y-5)=f(y)

Jun 24, 2012 | Mathsoft StudyWorks! Mathematics Deluxe...

In Algebra

Likewise when you see

Special Binomial Products So when you multiply binomials you get ... Binomial Products

And we are going to look at

1. Multiplying a Binomial by Itself What happens when you square a binomial (in other words, multiply it by itself) .. ?

(a+b)2 = (a+b)(a+b) = ... ?

The result:

(a+b)2 = a2 + 2ab + b2

You can easily see why it works, in this diagram:

2. Subtract Times Subtract
And what happens if you square a binomial with a **minus** inside?

(a-b)2 = (a-b)(a-b) = ... ?

The result:

(a-b)2 = a2 - 2ab + b2

3. Add Times Subtract
And then there is one more special case... what if you multiply (a+b) by (a-b) ?

(a+b)(a-b) = ... ?

The result:

(a+b)(a-b) = a2 - b2

That was interesting! It ended up very simple.

And it is called the "**difference of two squares**" (the two squares are **a2** and **b2**).

This illustration may help you see why it works:

a2 - b2 is equal to (a+b)(a-b)
Note: it does not matter if (a-b) comes first:

(a-b)(a+b) = a2 - b2

The Three Cases
Here are the three results we just got:

(a+b)2
= a2 + 2ab + b2
} (the "perfect square trinomials")
(a-b)2
= a2 - 2ab + b2
(a+b)(a-b)
= a2 - b2
(the "difference of squares")
Remember those patterns, they will save you time and help you solve many algebra puzzles.

Using Them
So far we have just used "a" and "b", but they could be anything.

Example: (y+1)2

We can use the (a+b)2 case where "a" is y, and "b" is 1:

(y+1)2 = (y)2 + 2(y)(1) + (1)2 = y2 + 2y + 1

Example: (3x-4)2

We can use the (a-b)2 case where "a" is 3x, and "b" is 4:

(3x-4)2 = (3x)2 - 2(3x)(4) + (4)2 = 9x2 - 24x + 16

Example: (4y+2)(4y-2)

We know that the result will be the difference of two squares, because:

(a+b)(a-b) = a2 - b2

so:

(4y+2)(4y-2) = (4y)2 - (2)2 = 16y2 - 4

Sometimes you can recognize the pattern of the answer:

Example: can you work out which binomials to multiply to get 4x2 - 9

Hmmm... is that the difference of two squares?

Yes! **4x2** is **(2x)2**, and **9** is **(3)2**, so we have:

4x2 - 9 = (2x)2 - (3)2

And that can be produced by the difference of squares formula:

(a+b)(a-b) = a2 - b2

Like this ("a" is 2x, and "b" is 3):

(2x+3)(2x-3) = (2x)2 - (3)2 = 4x2 - 9

So the answer is that you can multiply **(2x+3)** and **(2x-3)** to get **4x2 - 9**

Jul 26, 2011 | Computers & Internet

That is an equation describing a straight line. The "slope-intercept" form of a line is

y = mx + b

where m is the slope (change in y-value / change in x-value)

and b is the y-intercept (the point where the line crosses the y-axis when x=0)

Positive slope means the line is rising and negative slope means it's falling.

You can rewrite the original equation 2x - 4y -9 = 0 in slope-intercept form:

y = (1/2)x - (9/4)

So you know the slope is positive 1/2 (line rises 1 y-unit for each 2 x-unit change) and crosses the y-axis at -9/4. With this information you can graph the line.

y = mx + b

where m is the slope (change in y-value / change in x-value)

and b is the y-intercept (the point where the line crosses the y-axis when x=0)

Positive slope means the line is rising and negative slope means it's falling.

You can rewrite the original equation 2x - 4y -9 = 0 in slope-intercept form:

y = (1/2)x - (9/4)

So you know the slope is positive 1/2 (line rises 1 y-unit for each 2 x-unit change) and crosses the y-axis at -9/4. With this information you can graph the line.

Jul 12, 2011 | Sewing Machines

what is the value of x?

if x = 1 in the equation then,

1 = 4y+5

1 - 5 = 4y

-4 = 4y

y = -4/4

y = -1

if x = 1 in the equation then,

1 = 4y+5

1 - 5 = 4y

-4 = 4y

y = -4/4

y = -1

Jun 30, 2011 | Computers & Internet

2x + 4y = -8 ; divide each side by 2

x + 2y = -4 ; subtract x from both sides

2y = -4 - x ; rearrange

2y = -1x -4 ; divide each side by 2

y = -1/2x - 2 ; relate to slope/intercept form of line (y=mx+b)

implies there are multiple solutions that fall along a line with slope -1/2 and y intercept of -2

'

\ '

++++++++++

\ '

\ '

Sample points on this line are (-4,0), (-2,-1), (0,-2), (2,-3)

x + 2y = -4 ; subtract x from both sides

2y = -4 - x ; rearrange

2y = -1x -4 ; divide each side by 2

y = -1/2x - 2 ; relate to slope/intercept form of line (y=mx+b)

implies there are multiple solutions that fall along a line with slope -1/2 and y intercept of -2

'

\ '

++++++++++

\ '

\ '

Sample points on this line are (-4,0), (-2,-1), (0,-2), (2,-3)

Nov 04, 2010 | Mathsoft StudyWorks! Mathematics Deluxe...

You can solve it with following method.

5x+3y=6 2x-4y=5

So 5x=6-3y so 2[(6-3y)/5]-4y=5

So x=(6-3y)/5 so 12-6y-20y=25

so -26y=25-12

so -26y=13

so y= -(1/2)

2x-4y=5

so 2x=5+4y

so 2x=5+4(-1/2)

so 2x=(10-4)/2

so 2x=6/4

so x =3/2

The value of x=3/2 and value of y= -1/2

Let me know if you need further assistance.

Thanks for using FixYa.

5x+3y=6 2x-4y=5

So 5x=6-3y so 2[(6-3y)/5]-4y=5

So x=(6-3y)/5 so 12-6y-20y=25

so -26y=25-12

so -26y=13

so y= -(1/2)

2x-4y=5

so 2x=5+4y

so 2x=5+4(-1/2)

so 2x=(10-4)/2

so 2x=6/4

so x =3/2

The value of x=3/2 and value of y= -1/2

Let me know if you need further assistance.

Thanks for using FixYa.

Mar 03, 2010 | Office Equipment & Supplies

2x-4y=8

=> 2[x-2y]=8

=> x-2y=8/2

=>** x-2y=4**

=> 2[x-2y]=8

=> x-2y=8/2

=>

Feb 07, 2010 | Mathsoft StudyWorks! Mathematics Deluxe...

See this solution http://www.fixya.com/support/t663157-calculate_equation,

also in the case of your example:

4y=2x4 (4 times y = 2 times x times 4, moving the 4 over makes it divide by 4)

y=__2x4__ (the 4's cancel out, 4 divided by 4 = 1, 1 times anything is the same)

4

so y=2x (if we move x over it becomes divide by)

so__y__=2 (y diveided by x = 2 is as far as you can go)

x

also in the case of your example:

4y=2x4 (4 times y = 2 times x times 4, moving the 4 over makes it divide by 4)

y=

4

so y=2x (if we move x over it becomes divide by)

so

x

Jun 26, 2008 | Casio FX-300MS Calculator

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