Question about MathRescue Word Problems Of Algebra Lite

Given "2R-3S=-10", then "6R-9S=-30".

Given "3R 2S=37", then "6R 4S=74".

Subtract the two equations: "6R-6R 4S --9S = 74 --30",

which reduces to: "4S --9S=104".

Note that 'R' has been eliminated from the equation, as requested.

Solving for 'S' is left as an exercise for the reader.

Posted on Sep 03, 2010

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Posted on Jan 02, 2017

To solve a system of equations, there are two algebraic ways to solve them, one is by substitution, while the other is elimination.

1) 2a + 3b + 5 = 0

2) 2a + 4b + 10 = 0

-----------------------

-b -5 = 0 (subtract 2 from 1)

+b-b-5 = b

-5 = b

Substitute into 1) to solve for a.

2a + 3(-5) + 5 = 0

2a -15 + 5 = 0

2a -10 = 0

2a -10 + 10 = 10

2a = 10

---- ----

2 2

a=5

Substitute into 2) to check if we did it correctly.

2(5) + 4(-5) + 10 = 0

10 -20 + 10 = 0

0=0

Good luck.

Paul

1) 2a + 3b + 5 = 0

2) 2a + 4b + 10 = 0

-----------------------

-b -5 = 0 (subtract 2 from 1)

+b-b-5 = b

-5 = b

Substitute into 1) to solve for a.

2a + 3(-5) + 5 = 0

2a -15 + 5 = 0

2a -10 = 0

2a -10 + 10 = 10

2a = 10

---- ----

2 2

a=5

Substitute into 2) to check if we did it correctly.

2(5) + 4(-5) + 10 = 0

10 -20 + 10 = 0

0=0

Good luck.

Paul

Feb 10, 2015 | Office Equipment & Supplies

Simplifying

Y = 30x + 450

Reorder the terms:

Y = 450 + 30x

Solving

Y = 450 + 30x

Solving for variable 'Y'.

Move all terms containing Y to the left, all other terms to the right.

Simplifying

Y = 450 + 30x

Y = 30x + 450

Reorder the terms:

Y = 450 + 30x

Solving

Y = 450 + 30x

Solving for variable 'Y'.

Move all terms containing Y to the left, all other terms to the right.

Simplifying

Y = 450 + 30x

Mar 07, 2014 | Pee-Eww Urine Elimination System

The FX-901 calculator seems to be the equivalent of the FX 260 Solar sold in North America. It does fraction calculations, permutation, statistics but lack the Equation Solver.

You cannot use it to solve equations.

Casio Scientific calculators that can handle equation solving are the FX-115 and FX-991.

Simplify your first equation by dividing all its terms by 3, then use elimination to carry out the solution by hand.

You cannot use it to solve equations.

Casio Scientific calculators that can handle equation solving are the FX-115 and FX-991.

Simplify your first equation by dividing all its terms by 3, then use elimination to carry out the solution by hand.

Sep 02, 2012 | Office Equipment & Supplies

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...

Apply what you learned, especially that this system is quite simple.

Elimination

1. entails eliminating one variable to find (in this case) a single equation involving the other variable.

2. Solve that new equation, meaning isolate the variable that was not eliminated.

3. Substitute the value found in the last step and replace it in one of the original equation to obtain the other variable.

x+y=10

x-y=-6

Add the left sides to get x+y+x-y=2x

Add the right sides of the system to obtain 10+(-6)=4

Write Sum of left sides =Sum of right sides or 2x=4.

Since this new equation involves only x, you can solve it for x, getting x=4/2=2

Now you know the value of x (=2)

Take one of the original equations (for example x+y=10) and put 2 in place of x.

The equation becomes 2+y=10

Solve it to obtain y=10-2=8

Thus your solution is x=2, y=8

Check: use one equation in which you substitute 2 for x and 8 for y: x-y=-6 becomes 2-8=-6

Verified.

In the general case you will have to multiply by certain values to obtain opposite coefficients for the same variable. Here that was not necessary because the coefficient of y is 1 in the first equation and -1 in the second.

Elimination

1. entails eliminating one variable to find (in this case) a single equation involving the other variable.

2. Solve that new equation, meaning isolate the variable that was not eliminated.

3. Substitute the value found in the last step and replace it in one of the original equation to obtain the other variable.

x+y=10

x-y=-6

Add the left sides to get x+y+x-y=2x

Add the right sides of the system to obtain 10+(-6)=4

Write Sum of left sides =Sum of right sides or 2x=4.

Since this new equation involves only x, you can solve it for x, getting x=4/2=2

Now you know the value of x (=2)

Take one of the original equations (for example x+y=10) and put 2 in place of x.

The equation becomes 2+y=10

Solve it to obtain y=10-2=8

Thus your solution is x=2, y=8

Check: use one equation in which you substitute 2 for x and 8 for y: x-y=-6 becomes 2-8=-6

Verified.

In the general case you will have to multiply by certain values to obtain opposite coefficients for the same variable. Here that was not necessary because the coefficient of y is 1 in the first equation and -1 in the second.

Aug 16, 2011 | Casio Office Equipment & Supplies

This calculator cannot handle matrices that have anyone dimension larger than 3.

How to solve your problem?

use a computer program devoted to solving linear equations

OR buy another calculator that can handle larger systems of equations (a graphing calculator, maybe).

How to solve your problem?

- Set up the problem by hand (pencil paper): use Cramer's rules. Make use of the calculator to perform the various calculation.

- Sacrifice one equation which you will use to eliminate one variable of the 4 by expressing it in terms of the other three. Do the algebra to obtain a system of 3 equations in three unknowns.
- Use the calculator to find the solutions ( the three variables that are left).
- Use the 4th equation (the one you scacrificed) to obtain the value of the 4th unknown.

use a computer program devoted to solving linear equations

OR buy another calculator that can handle larger systems of equations (a graphing calculator, maybe).

Feb 16, 2011 | Casio FX-115ES Scientific Calculator

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

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

Hello,

Let us assume you have two simultaneous linear equations :

**a_1*x+ b_1*y+c_1=0**

a_2*x +b_2*y+c_2=0

where a_1, a_2, b_1, b_2, c_1,c_2 are coefficients (numerical or algebraic).

The problem is to obtain the particular values of the unknowns x and y for which the two equations are both satisfied: If you substitute the particular values of x and y you find in any of the two equations you discover that both equalities are true.

A small system of equations like the one above can be solved by some very simple algorithms (elimination, substitution, combination) which can be carried out by hand.

The solution of large systems of linear equations can be sought by making use of the concepts of matrices (plural of matrix), determinants, and certain rules called Cramer's rules.

Due to its repetitive nature, the algorithm ( a well defined, limited sequence of steps) is suitable for a calculating machine (computer or calculator).

Certain calculators have, embedded in their ROM, a program that solves linear systems of simultaneous equations. Usually you are asked to enter the values of the coefficients a_1, etc. in a set order, then you press ENTER or EXE (Casio) . If a solution exits (not all linear systems have solutions) the calculator displays it.

Hope that satisfies your curiosity.

Let us assume you have two simultaneous linear equations :

a_2*x +b_2*y+c_2=0

where a_1, a_2, b_1, b_2, c_1,c_2 are coefficients (numerical or algebraic).

The problem is to obtain the particular values of the unknowns x and y for which the two equations are both satisfied: If you substitute the particular values of x and y you find in any of the two equations you discover that both equalities are true.

A small system of equations like the one above can be solved by some very simple algorithms (elimination, substitution, combination) which can be carried out by hand.

The solution of large systems of linear equations can be sought by making use of the concepts of matrices (plural of matrix), determinants, and certain rules called Cramer's rules.

Due to its repetitive nature, the algorithm ( a well defined, limited sequence of steps) is suitable for a calculating machine (computer or calculator).

Certain calculators have, embedded in their ROM, a program that solves linear systems of simultaneous equations. Usually you are asked to enter the values of the coefficients a_1, etc. in a set order, then you press ENTER or EXE (Casio) . If a solution exits (not all linear systems have solutions) the calculator displays it.

Hope that satisfies your curiosity.

Aug 12, 2009 | Sharp EL-531VB Calculator

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Apr 27, 2009 | Casio CFX-9850G Plus Calculator

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