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Browse High School Linear Equations
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Diophantine equations.
    Solving simple linear equations.

Positive Unit Fractions [10/02/2002]

Probability of a Sum Meeting a Condition [08/24/2007]
Two real numbers from 0 to 12 are randomly chosen. Find the probability that their sum is less than or equal to 5.

Probate Puzzle [12/15/2003]

Quadratic Equation [04/08/1997]

Quadratic Equation [7/10/1996]
Why is a quadratic equation "quadratic"?

Quadratic Equations [12/3/1995]



Second-Degree Two-Variable Diophantine Equation [04/12/2001]
Solve Ax^2+Bxy+Cy^2+Dx+Ey+F = 0 where B^2-4AC=k^2 for some integer k.

Simultaneous Equations [07/01/2002]

Simultaneous Equations and the Addition Method [06/01/1998]
Solving two unknowns in two equations.

Simultaneous Equations with Floor and Remainder Functions [12/10/2001]
Let x, y, z be three positive real numbers such that x+[y]+{z}=13.2; [x]+{y}+z=14.3; {x}+y+[z]=15.1 ... Find the value of x.

Slopes of Perpendicular Lines [09/17/1998]
Why are the slopes of perpendicular lines negative reciprocals?

Solutions to Linear Equations [09/21/2001]
Can you specify the conditions under which a a system of linear equations has infinitely many solutions, a unique solution and no solution?

Solve for x; Find 5 Ordered Pairs [11/01/2002]
Two questions: Determine 5 ordered pairs that will satisfy the equation 4y = 8 - 2x. Solve for x: 3x/4 - 4 = 7 + x/2.

Solve for x, y, and z [7/27/1996]
How do I solve for x, y, and z in these three equations: 1/2y + 1/3z = 26, 1/3x + 1/4z = 23, and 1/2x + 1/4y = 28?


Solving Equations with Square Roots [03/28/2003]
When solving x + 1 = sqrt(x + 3), we can square both sides then solve the equation; however, we get an extra solution that doesn't work. Why?

Solving for One Variable of Many [05/30/2002]
How do you solve a formula with many variables for one of them?

Solving Multivariable Diophantine Equations [05/03/1998]
Finding general solutions to two diophantine equations.

Solving Pairs of Equations by Substitution [11/26/1997]
x + 3y = - 5; 3x - 2y = 7.

Solving Systems of Linear Equations [02/09/1999]
Can you help me solve simultaneous equations?

Solving Systems of Linear Equations by Combination [11/11/2003]
An introduction to effectively using the combination method to solve a system of linear equations, for any number of equations and variables.

Speedometer Error and Tire Size [07/13/1999]
I need to know my exact speed at a given rpm based on tire size. How do I figure my speed in miles per hour?

Standard Form Equation of a Line [01/05/2007]
In the equation of a line, such as 2x - y + 3 = 0, why does the x term always have to have a positive coefficient? Why can't that equation be written as -2x + y - 3 = 0? Isn't that the same equation?

Standard Form of a Line [04/23/2002]
What is standard form? What does Ax+by = c mean and what do the letters stand for?

Standard Form of a Line (Ax + By = C) [10/07/2005]
In the standard form of a linear equation, Ax + By = C, what conditions do A, B, and C have to meet? Do you always have to have a positive integer for A? Do you have to have all the common factors of A, B, and C factored out?

Straight Line on the Graph [09/10/1998]
Let f(x) = ae^(kx) where a>0 and k are constants. Show that the graph of y = ln(f(x)) is a straight line.

Substituting in the Point-Slope Form of a Linear Equation [02/05/2005]
In the point-slope equation y - y1 = m(x - x1), why is the point you are using, such as (3,-5), always substituted for the y1 and x1? Why can't it be substituted for the 'plain' x and the 'plain' y?

Substituting Parameters for Numbers [11/29/2001]
I don't know what to do with both sides of the equation 17.20X/100 = X- 579.59.

Subtracting One Equation from Another [05/30/2001]
Why can you subtract one equation from another and get something meaningful that you can use to solve the equations?

The Sum of Two Numbers is 20... [11/03/1997]
Twice one number is 4 more than four times the other. Find the numbers.

Switching Dollars and Cents [10/07/1997]
How do I find an equation?

System Of Equations With Products Of Variables [10/29/2003]
I'm trying to solve a system of three equations and three variables where the variables are multiplied together, such as 'xy' and 'yz'. Substitution doesn't seem to be working very well - what's a good way to get started?

Systems of Linear Equations [11/3/1994]
It has been some time since I took algebra and my son has asked me the following question: Solve for each system of equations. . .

Systems with More Variables than Equations [12/11/2002]
How do I solve a system that has three variables and only two equations, such as 187y + 98x + 45z = 48 and 2y + 9x + 3z = 198?

Trains, Times, and Tunnel Vision: Thinking beyond Formulas [06/28/2010]
A student seeks a formula to solve a "two trains" word problem. Rather than indulge in formulaic thinking, Doctor Ian suggests using related rates to make the problem simpler.

Transposing Equations [07/14/1998]
I am having trouble when transposing. When y = 2x + 3, how do you find the value of x?

Two Equations with Two Unknowns [05/24/1999]
How do you solve simultaneous equations?

Typical Algebraic Linear Programming Problem [08/07/2004]
Determine how many of each type of employee should be hired to complete a specific job and minimize the labor expenses.


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