Question about Educational & Reference Software

It would be easier to add the first and last number, divide by two (you are finding the average), and multiply by the amount of numbers in the sequence (100). It is a formula, but it is an easier way to remember it.

Posted on May 13, 2009

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...

Being parallel to the given line, the equation of the line you are seeking has the same slope, which in this case is **a=1/4.**

So the equation sought is as follows

y=**(1/4)x** +b, where b is to be found.

To find** b**, use the stated fact that the line passes through the point **(x=8, y=-1)**. All that means is that the point **(8,-1)** is on the line whose equation you are looking for. If it is on the line with equation **y=(1/4)x+b**

then its coordinates x=8, and y=-1 satisfy the relation y=(1/4)x+b. In other words, if you substitute 8 for x, and -1 for y, the equality holds true**-1=(1/4)*8 +b**

This gives you a way to find the initial value of the function (the y-intercept b ). Just solve**-1=(1/4)*8 +b** to find b.

I leave this pleasure to you.

So the equation sought is as follows

y=

To find

then its coordinates x=8, and y=-1 satisfy the relation y=(1/4)x+b. In other words, if you substitute 8 for x, and -1 for y, the equality holds true

This gives you a way to find the initial value of the function (the y-intercept b ). Just solve

I leave this pleasure to you.

Jan 15, 2014 | Mathsoft StudyWorks! Mathematics Deluxe...

The following are examples of expressions:

2

*x*

3 + 7

2 ×*y* + 5

2 + 6 × (4 - 2)

*z* + 3 × (8 - *z*)

Example:

Roland weighs 70 kilograms, and Mark weighs*k* kilograms. Write an expression
for their combined weight. The combined weight in kilograms of these two people
is the sum of their weights, which is 70 + *k*.

Example:

A car travels down the freeway at 55 kilometers per hour. Write an expression for the distance the car will have traveled after*h* hours. Distance equals rate
times time, so the distance traveled is equal to 55 × *h*..

Example:

There are 2000 liters of water in a swimming pool. Water is filling the pool at the rate of 100 liters per minute. Write an expression for the amount of water, in liters, in the swimming pool after*m* minutes. The amount of water added
to the pool after *m* minutes will be 100 liters per minute times *m*,
or 100 × *m*. Since we started with 2000 liters of water in the pool,
we add this to the amount of water added to the pool to get the expression 100 ×
*m *+ 2000.

To evaluate an expression at some number means we replace a variable in an expression with the number, and simplify the expression.

Example:

Evaluate the expression 4 ×*z* + 12 when *z* = 15.

We replace each occurrence of*z* with the number 15, and simplify using the
usual rules: parentheses first, then exponents, multiplication and division, then
addition and subtraction.

4 ×*z* + 12 becomes

4 × 15 + 12 =

60 + 12 =

72

Example:

Evaluate the expression (1 +*z*) × 2 + 12 ÷ 3 - *z* when
*z* = 4.

We replace each occurrence of z with the number 4, and simplify using the usual rules: parentheses first, then exponents, multiplication and division, then addition and subtraction.

(1 +*z*) × 2 + 12 ÷ 3 - *z* becomes

(1 + 4) × 2 + 12 ÷ 3 - 4 =

5 × 2 + 12 ÷ 3 - 4 =

10 + 4 - 4 =

10.

**hope that help you**

2

3 + 7

2 ×

2 + 6 × (4 - 2)

Example:

Roland weighs 70 kilograms, and Mark weighs

Example:

A car travels down the freeway at 55 kilometers per hour. Write an expression for the distance the car will have traveled after

Example:

There are 2000 liters of water in a swimming pool. Water is filling the pool at the rate of 100 liters per minute. Write an expression for the amount of water, in liters, in the swimming pool after

To evaluate an expression at some number means we replace a variable in an expression with the number, and simplify the expression.

Example:

Evaluate the expression 4 ×

We replace each occurrence of

4 ×

4 × 15 + 12 =

60 + 12 =

72

Example:

Evaluate the expression (1 +

We replace each occurrence of z with the number 4, and simplify using the usual rules: parentheses first, then exponents, multiplication and division, then addition and subtraction.

(1 +

(1 + 4) × 2 + 12 ÷ 3 - 4 =

5 × 2 + 12 ÷ 3 - 4 =

10 + 4 - 4 =

10.

Jun 22, 2011 | LeapFrog Turbo Twist Math Cartridge 5th...

Definition

A mathematical statement used to evaluate a value. An equation can use any combination of mathematical operations, including addition, subtraction, division, or multiplication. An equation can be already established due to the properties of numbers (2 + 2 = 4), or can be filled solely with variables which can be replaced with numerical values to get a resulting value. For example, the equation to calculate return on sales is: Net income ÷ Sales revenue = Return on Sales. When the values for net income and sales revenue are plugged into the equation, you are able to calculate the value of return on sales.

There are many types of mathematical equations.

1. Linear Equations y= mx + b (standard form of linear equation)

2. Quadratic Equations y= ax^2+bx+c

3. Exponential Equations y= ab^x

4. Cubic Equations y=ax^3+ bx^2+cx+d

5. Quartic Equations y= ax^4+ bx^3+ cx^2+ dx+ e

6. Equation of a circle (x-h)^2+(y-k)^2= r^2

7. Constant equation y= 9 (basically y has to equal a number for it to be a constant equation).

8. Proportional equations y=kx; y= k/x, etc.

Jun 14, 2011 | Educational & Reference Software

this is a simple algebraic equation in which we have to calculate the value of 'x' using simple operations

7+(9-5x)=5(2-x)

step 1(pen the brackets) 7+9-5x=10-5x

step 2(add 7 and 9) 16-5x=10-5x

now as 5x gets cancelled both the sides of the equal sign therefore no solution of this algebraic equation exist.

7+(9-5x)=5(2-x)

step 1(pen the brackets) 7+9-5x=10-5x

step 2(add 7 and 9) 16-5x=10-5x

now as 5x gets cancelled both the sides of the equal sign therefore no solution of this algebraic equation exist.

Mar 24, 2011 | MathRescue Word Problems Of Algebra Lite

__The 1st equation contains a ‘+y’, while the 2nd contains a ‘-y’ term. they will cancel if added together, so we will add the equations to eliminate ‘y’.____x-y=2____x+y=10____so add them together__

__(x-y)+(x+y)=12____2x = 12____X= 12/2 = 6____subsitutue for____6+y=10____y=10-6=4____Answer X = 6 and Y = 4__

Apr 11, 2010 | SoftMath Algebrator - Algebra Homework...

Solve the following equation, for X between 0 and 9, inclusive,

and for Y between 0 and 9, inclusive:

7*1 + 1*10 + x* 100 + 3*1000 + y*10*1000 + 9* 100*1000

How many different answers are possible:

(a) none

(b) 10

(c) 20

(d) 99

(e) 100

(f) none of the above

???

and for Y between 0 and 9, inclusive:

7*1 + 1*10 + x* 100 + 3*1000 + y*10*1000 + 9* 100*1000

How many different answers are possible:

(a) none

(b) 10

(c) 20

(d) 99

(e) 100

(f) none of the above

???

Nov 29, 2009 | The Learning Company Achieve! Math &...

Allan is 19 and Roy is 13.

Solution:

First we have 2 variables, their ages: I used Allan = x & Roy = y

Equation 1: X - 4 = 2*(Y-4) - 3

We can ignore the 5 years in the second part of the statement. Allan will always be 6 years older than Roy whether it be 5 years from now or ten years form now.

Equation 2: X = Y + 6

Substitute Y + 6 for X in equation 1:

X - 4 = 2*(Y-4) - 3 becomes Y + 6 - 4 = 2*(Y-4) - 3

That simplifies to Y + 2 = 2Y - 8 - 3

Rewrite it again: Y + 2 = 2Y - 11

Add 11 to both sides: Y + 13 = 2Y

Subtract Y from both sides: 13 = Y

Now plug 13 in for y in Equation 2

X = Y + 6

X = 13 + 6

X = 19

Solution:

First we have 2 variables, their ages: I used Allan = x & Roy = y

Equation 1: X - 4 = 2*(Y-4) - 3

We can ignore the 5 years in the second part of the statement. Allan will always be 6 years older than Roy whether it be 5 years from now or ten years form now.

Equation 2: X = Y + 6

Substitute Y + 6 for X in equation 1:

X - 4 = 2*(Y-4) - 3 becomes Y + 6 - 4 = 2*(Y-4) - 3

That simplifies to Y + 2 = 2Y - 8 - 3

Rewrite it again: Y + 2 = 2Y - 11

Add 11 to both sides: Y + 13 = 2Y

Subtract Y from both sides: 13 = Y

Now plug 13 in for y in Equation 2

X = Y + 6

X = 13 + 6

X = 19

Oct 08, 2009 | Vivendi Math Blaster Algebra (03763) for...

2y - x = 3

x = 3y - 5

Add the two equations side by side,

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

2y = 3y - 2

y = 2

Plug this in the second equation to get x,

x = 3(2) - 5

x = 1

So the solution is**x = 1**, **y = 2**

or in ordered pair notation**(1, 2)**

x = 3y - 5

Add the two equations side by side,

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

2y = 3y - 2

y = 2

Plug this in the second equation to get x,

x = 3(2) - 5

x = 1

So the solution is

or in ordered pair notation

Jun 29, 2009 | Educational & Reference Software

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...

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