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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.

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 directly comparing the 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 Absolute Speeds versus a Single Relative One [08/06/2017]
A teen gets turned around modeling a question about two cars traveling the same direction at different speeds. With insights into proportional reasoning and frames of reference, Doctor Ian progressively steers her back to the path.

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.

Un-learning Unknowns [10/12/2010]
After solving a system of equations, a student realizes, "I have simply been going through the motions." Emphasizing that we make choices about how to solve and represent word problems, Doctor Peterson peels away rote notions about variables.

Using an Augmented Matrix [11/21/1999]
Solve the set of simultaneous equations x+3y+z=3, x+5y+5z=1 and 2x+6y+ 3z=8 using an augmented matrix?

Variation on Combined Work [06/13/2002]
If you run a large pipe for 4 hours, and run a small pipe for 9 hours, you can fill 1/2 a pool. If you run both pipes together for 12 hours, you can fill the whole pool. How long would it take to fill the pool using each pipe by itself?

Vectors and Linear Combinations [01/25/1999]
If vector v0 = (x0, y0, z0) and vector v1 = (x1, y1, z1) both satisfy ax + by + cz = d, then why does mv0 + nv1, where m + n = 1, satisfy that equation too?

Volume by Inch of a Cone-Shaped Tank [03/03/2003]
I have a chemical tank that has a cone bottom and I need to know the volume of each inch of the cone.

A Way to Estimate the Square Root of Any Number [03/16/2006]
A student studying square roots discovers an interesting method of estimating non-perfect roots and is curious why it works.

A Way to Remember What 'm' and 'b' Mean in Slope-Intercept Form [02/01/2004]
An interesting memory trick to help you remember how to graph a linear equation in slope-intercept form.

What is Nonlinear Math? [10/02/1997]
What exactly is nonlinear math, and what is it used for?

When is a Slope 0 or Undefined? [3/29/1997]
How do I know when the slope of an equation is zero or undefined (no slope)?

Why b for Intercept? [10/16/2003]
In the slope-intercept formula, y = mx + b, why is 'b' used to represent the y-intercept?

Why Does Adding Equations to Solve a System Work? [02/10/2007]
I know you can add two linear equations together to eliminate one variable as part of solving a system of equations, but I don't understand why that works. Are you adding the lines together? What does the resulting equation represent in terms of the original lines?

Why Does the Slope Formula Work? [10/29/2008]
How does the slope formula (y2 - y1)/(x2 - x1), which uses subtraction and division, come up with a slope?

Why is 'b' Used in Slope-Intercept Form? [02/04/2004]
Why is the letter 'b' used for the y-intercept in the slope-intercept form of a linear equation?

Why Is Slope Rise Over Run and Not Run Over Rise? [03/05/2005]
We were wondering today in math class why slope is defined as rise over run and why it couldn't be run over rise?

X- and Y-Intercepts [09/15/1998]
I'm having a hard time finding out how to solve an equation and then do the graph. The intercepts confuse me also...

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