If you earned an average of 25,000 over your working life and you retire after 2005 at age 62,63,or 64 , then your annual social security benefit will be $7000, $7500, or $8000. There is a linear equation that gives the annual benefit b in terms of age a for these three years, find the equations

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Posted on Jan 02, 2017

The Internal Revenue Service says you can figure out whether you have to pay taxes on Social Security by adding half of your annual benefit to your other income. If the total is more than $32,000 and you file a joint return, some of your benefits must be reported as taxable income on your tax return. For single filers the threshold is $25,000. For example, if you file as single and your annual benefit is $15,000, half of your benefit amount is $7,500. You you can earn up to $17,500 in additional income before you hit the $25,000 mark and have to pay taxes on Social Security benefits.

Feb 12, 2015 | Cars & Trucks

For two linear equations, one can use

comparison, substitution, or addition/combination.

For more linear equations one uses the Cramer Rule that involves matrices and their determinants.

comparison, substitution, or addition/combination.

For more linear equations one uses the Cramer Rule that involves matrices and their determinants.

Sep 16, 2014 | Office Equipment & Supplies

Hi there,

You cannot solve linear equations on a SHARP EL531. If you would like a calculator that solves equations, you need to get a SHARP EL W506

You cannot solve linear equations on a SHARP EL531. If you would like a calculator that solves equations, you need to get a SHARP EL W506

Apr 08, 2014 | Sharp el-531x scientific calculator

Thhe Casio FX-9860G SD can solve a polynomial equation
of degree 2 or 3 with REAL coefficients. If the complex MODE is set to
REAL it will find the real roots. If the complex mode is set to** a+ib**, it will find the real and complex roots.

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

Addendum.

The calculator CANNOT solve equations with complex coefficient. YOU can however convert the system of linear equations with ccomplex coefficients ( of the type you show) as a system of 4 linear equations in 4 unknowns; Split x into a real and an imaginary part, split y into a real and an imaginary part. Substitute Real(x)+iIm(x) for variable x in the equations; substitute Real(y)+iIm(y) for y in the two equations; do the algebra. In each of the original equations split the Real and imaginary parts. You should be able to derive 4 linear equations in unknowns Real(x), Im(x), Real(y), and Im(y).

Use the linear equation solver to obtain the solutions. Recompose x=Real(x)+iIm(x), and y=Real(y)+iIm(y)

Alternatively, after you create the system of 4 linear equations you can use the matrix utility to find Real(x), Im(x), Real(y) and Im(y) and recompose the x and y.

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

Addendum.

The calculator CANNOT solve equations with complex coefficient. YOU can however convert the system of linear equations with ccomplex coefficients ( of the type you show) as a system of 4 linear equations in 4 unknowns; Split x into a real and an imaginary part, split y into a real and an imaginary part. Substitute Real(x)+iIm(x) for variable x in the equations; substitute Real(y)+iIm(y) for y in the two equations; do the algebra. In each of the original equations split the Real and imaginary parts. You should be able to derive 4 linear equations in unknowns Real(x), Im(x), Real(y), and Im(y).

Use the linear equation solver to obtain the solutions. Recompose x=Real(x)+iIm(x), and y=Real(y)+iIm(y)

Alternatively, after you create the system of 4 linear equations you can use the matrix utility to find Real(x), Im(x), Real(y) and Im(y) and recompose the x and y.

Mar 17, 2012 | Casio FX-9860G Graphic Calculator

The Casio FX-9860G SD can solve a polynomial equation
of degree 2 or 3 with REAL coefficients. If the complex MODE is set to
REAL it will find the real roots. If the complex mode is set to** a+ib**, it will find the real and complex roots.

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

Addendum.

The calculator CANNOT solve equations with complex coefficient. YOU can however convert the system of linear equations with ccomplex coefficients ( of the type you show) as a system of 4 linear equations in 4 unknowns; Split x into a real and an imaginary part, split y into a real and an imaginary part. Substitute Real(x)+iIm(x) for variable x in the equations; substitute Real(y)+iIm(y) for y in the two equations; do the algebra. In each of the original equations split the Real and imaginary parts. You should be able to derive 4 linear equations in unknowns Real(x), Im(x), Real(y), and Im(y).

Use the linear equation solver to obtain the solutions. Recompose x=Real(x)+iIm(x), and y=Real(y)+iIm(y)

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

Addendum.

The calculator CANNOT solve equations with complex coefficient. YOU can however convert the system of linear equations with ccomplex coefficients ( of the type you show) as a system of 4 linear equations in 4 unknowns; Split x into a real and an imaginary part, split y into a real and an imaginary part. Substitute Real(x)+iIm(x) for variable x in the equations; substitute Real(y)+iIm(y) for y in the two equations; do the algebra. In each of the original equations split the Real and imaginary parts. You should be able to derive 4 linear equations in unknowns Real(x), Im(x), Real(y), and Im(y).

Use the linear equation solver to obtain the solutions. Recompose x=Real(x)+iIm(x), and y=Real(y)+iIm(y)

Mar 17, 2012 | Casio Office Equipment & Supplies

let c = cory's age now
let s = her sisters age now

cory's age now = sisters age + 6 years

=> c = s + 6

4 years ago, cory was 4 years younger ( i.e. c-4) and her sister was 4 years younger (s- 4)

4 years ago cory was 4 times older than her sister

=> c - 4 = 4*(s-4)

We can simplify this to c = 4s - 16 +4 c = 4s - 12

We can then use simultaneous equations to solve the two equations

(i) c = s + 6 (ii) c = 4s - 12

If we multiply both sides of equation (i) by 4 we get (iii) 4c = 4s + 24

We can then subtract equation (ii) from equation (iii) to eliminate the '4s' term => ( 4c = 4s + 24 ) - (c = 4s - 12) => 4c - c = 4s +24 - 4s +12 => 3c = 4s - 4s +36 => 3c = 36 => c = 36/3 => c = 12 => Cory's age now = 12

__For clarity:__
Her sister's age now is of course 6
4 years ago Cory would of been 8 and her sister would of been 2

I hope this helps and good luck! If you have more questions - ask away!

Please take the time to rate this answer

Many Thanks Don.

cory's age now = sisters age + 6 years

=> c = s + 6

4 years ago, cory was 4 years younger ( i.e. c-4) and her sister was 4 years younger (s- 4)

4 years ago cory was 4 times older than her sister

=> c - 4 = 4*(s-4)

We can simplify this to c = 4s - 16 +4 c = 4s - 12

We can then use simultaneous equations to solve the two equations

(i) c = s + 6 (ii) c = 4s - 12

If we multiply both sides of equation (i) by 4 we get (iii) 4c = 4s + 24

We can then subtract equation (ii) from equation (iii) to eliminate the '4s' term => ( 4c = 4s + 24 ) - (c = 4s - 12) => 4c - c = 4s +24 - 4s +12 => 3c = 4s - 4s +36 => 3c = 36 => c = 36/3 => c = 12 => Cory's age now = 12

I hope this helps and good luck! If you have more questions - ask away!

Please take the time to rate this answer

Many Thanks Don.

Sep 13, 2011 | Sunburst My Mathematical Life Single...

Set Computational mode to EQN by pressing [MODE][5:EQN]

Select the type of equations you want to solve

Select the relevant otion and get ready to type in the coefficients (the a's, the b's, the c's etc`.)

For more general non-linear equations, use the SOLVE feature.

Select the type of equations you want to solve

Select the relevant otion and get ready to type in the coefficients (the a's, the b's, the c's etc`.)

For more general non-linear equations, use the SOLVE feature.

Feb 11, 2011 | Casio FX-115ES Scientific Calculator

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

x=7

y=-1

y=-1

Jan 30, 2009 | Bagatrix Algebra Solved! 2005 (105101) for...

A positive number is 5 times another number.If 21 is added to both the numbers,then one of the new numbers becomes twice the other number.What are the numbers

Nov 29, 2007 | Computers & Internet

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