Linear Equations

• Line problems [JADEDC, 12/1/1994]
  A student asks several questions about lines and their equations such as: Give the equation of a vertical line, and does the point 2,4 lie on the line with equation x-5/y-3=3?

• Patterns in Linear Systems [Chris, 11/12/2001]
  Given the equation 2x+5y=8, with the coefficients increasing by 3 each time, create linear systems that are similar using equations such as 3x+4y=5 or 4x+6y=8.

• Substituting in Linear Equations [Jeannette, 11/14/2001]
  I am given two equations, 2y = 5x + 8x and 3y = 4x + 9x, and told to substitute something. What should I do?

• Systems of Linear Equations [Gardner, 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. . .

• Solve for x, y, and z [Tirojava, 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?

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

• Linear Equations: Chemical Formulas [Meliebe, 10/31/1997]
  What are the numbers for the chemical formulas: H2O2 + O3 = H2O + O2?

• Linear Inequalities [Maura, 11/26/1997]
  How do I solve the problem (x-2)/(x+1)<(x-4)/(x-1) ?

• Inconsistent and Dependent Systems [Shoup, 12/07/1997]
  Write a second linear equation for y = 2x + 4 that would create an inconsistent system.

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

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

• Changing Equations To Slope-Intercept Form [Holly, 07/17/1998]
  Can you explain how to change equations into slope-intercept form? For example, 12(2x-1) - 5(3y+2) = 8?

• Straight Line on the Graph [Elsa, 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.

• Interpreting Slopes [Poss, 09/14/1998]
  Does the graph of each of these equations rise to the right, fall to the right, is it horizontal, or is it vertical?

• X- and Y-Intercepts [Haun, 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...

• The General Polynomial Function [Chaithaweep, 09/17/1998]
  How do you relate a polynomial like y=6x-2 to the general polynomial function? How do I graph and find the inverse of y=sqrt(2)?

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

• Formulas for the Equation of a Line [Michelle, 09/28/1998]
  Can you explain the meaning behind the point-slope formula? What about other formulas for the equation of a line?

• Pool Table Algebra [Roland, 10/21/1998]
  The y-axis, x-axis, x = 6, and y = 12 determine the sides of a pool table. Follow the path of a ball starting at the point (3,8).

• Parallel and Perpendicular Lines [Anonymous, 01/14/1999]
  How do you tell without graphing whether the graphs of these equations are parallel, perpendicular, or neither?

• Vectors and Linear Combinations [Doud, 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?

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

• Population and Percentage [Ian, 03/07/1999]
  Given population data, find the number of women in two different years.

• Determining Slope [Jaramillo, 05/19/1999]
  How do I find the slope of a line given the coordinates of two points?

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

• Speedometer Error and Tire Size [Sugarman, 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?

• Equation for Undefined Slope [Andy, 10/24/1999]
  How do you write an equation for a vertical line with an undefined slope? For example, a vertical line with an x-intercept of 8.

• Using an Augmented Matrix [Katie, 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?

• Gaussian Elimination [Harper, 01/11/2000]
  How can you solve a system of linear equations using Gaussian elimination?

• Point on a Line [Chris, 03/23/2001]
  Can you please tell me a formula to find if a point exists on a line? Both are in x,y form.

• Line and Unit Circle; Pythagorean Triples [Kennedy, 04/16/2001]
  If (X,Y) is a point in the 1st quadrant on the unit circle and m is the slope of the line passing through (X,Y) and the point (0,-1), how can I express the coordinates (X,Y) in terms of m? Can this be used to generate Pythagorean triples?

• Solutions to Linear Equations [Nanda, 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?

• Simultaneous Equations with Floor and Remainder Functions [Vincent, 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.

• Equation of a Line [Victor, 02/14/2002]
  Prove the point-slope equation property y-y1 = m(x-x1).

• Non-Linear Equations and Chaotic Systems [Andrew, 03/21/2002]
  Are any non-linear equations used to predict complex or chaotic systems such as traffic or flocking birds?