How are "Linear Equations in two variables" used in everyday life?
454465
One use is in economics and optimisation.   If you're running a farm which produces two different crops or a factory that manufactures two different products, there is usually an optimum amount of each product which maximises your profit.  Linear equations in two variables allow you to calculate the optimum.
962302
You tell an equation is linear if there's a simple relationship between "x" and "y".\n\nIf you can say that "y is 2 lots of x, plus some constant number" or "y is half of x plus some constant number", that's a linear relationship.\n\nNote that the constant number can be 0!\n\nWritten formally, that means y = ax + b, where "a" is the simple relationship and "b" is some constant number.\n\nIf you need to transform "x" in any other way, it's non-linear.
497371
http://en.wikipedia.org/wiki/Linear_equations\n\nhttp://en.wikipedia.org/wiki/Math
570575
In a diagram where x denotes the horizontal axis and y the vertical axis, linear equations with only one variable (x or y) is either a horizontal or vertical line.\n\nexample 1:\n\ny = 3 is a horizontal line that connects all points in the diagram which have the y-value 3.\n\nexample 2:\n\nx = 5 is a vertical line that connects all points in the diagram which have the x-value 5.\n\nI hope this is clear?
282293
The techniques used to solve systems of linear equations (substitution and elimination) tend to do a pretty good job of solving quadratic systems.\n\nThis page does a pretty good job of demonstrating how:
818907
Linear means that the relationship between two variables varies in the same way, except by a constant factor (A) and a constant offset (B).  y = A*x + B\n\nThe volume of water in a tank, and its mass are linearly related.  [m = p*V, where m is the mass, p (rho) is the density of water, which is constant (converted to the units of m and V), and V is the volume of water.  The units of m and V are usually kg and liters, or lbs and ft^3.]\n\nAny other kind of relationship is non-linear, which includes most every process in the real world.  Non-linear relationships usually seem to result from friction/entropy/inefficiency or from forces like magnetic fields, electric fields, or gravity, or well pretty much everything real.
128537
It's arbitrary.\n\nWe are used to "x" and "y" (and perhaps "z") being used as the variables, but we also need to have a representation of constants. Using a specific number would make it seem as though only that number works in the equation.
771447
It is an equation, the result of the equation is the function. The result may be plotted and it would be a linear function. The plot is a function of the form (equation). It is linear only if it works out to a stright line, which this does.\n\n"A linear function of x is a function of the form y = ax + b, where a and b are constants.  It's called a "linear" function because a plot of the x and y coordinates for which this equation is true takes the shape of a straight line"
846806
If you want a visual answer, a function of one variable is graphed by a line, wavy or however.  A function of two variables is graphed by a surface.  Obviously, equations with two variables take more work and effort to make anything out of them, than those with just one.
589722
Step 1: Solve one equation for one variable in terms of the other.\nStep 2: Plug that into the other equation and solve for the second variable.\nStep 3: Plug the second variable into the first equation and solve for the first variable.
417878
linear.  Linear means "to the first power", nonlinear means "to the second power (squared)", "to the third power" or higher (or some other function).  \n\nPerimeter of a square = 4 x length of side.\nwhich means \n4 x "length of side to the first power"\n\ndouble the length of the side and you double the perimeter; triple it and you triple the perimeter.
779994
If you are solving a system of linear equations (presumbale, two equations with two variables), then there are an infinite number of solutions if the graphs coincide, i.e. are the same.\n\nFor example, if I ask you to solve the system\n\n4x - 2y = 12\ny = 2x - 6\n\nby graphing, you should discover that ythe graphs are the same.  As such, this system has an infinite number of solutions.  Any ordered pair that makes the first equation true (and there are an infinite number of them) will also make the second equation true.\n\n\nI really have no idea what you are asking, but that seemed reasonable.
978722
You can't, algebraically.  You have two equations and three variables.  Sorry.  You need one more equation, such as a = b.
164074
alright, finally a question i can answer, ok first of all u need some bivariate data (meaning data in the first two lists). exponential regression is going to find the equation of the line that best fits the data. on my calc there is linear regression (straight line), quadratic regression (parabola looking thing), cubic regression (cubic looking thing), quartic regression (weird looking parabola), and ooo i see what ur talking about. hmm i think its like finding an equation of the line then looks like an exponential equation. and example of this is graphing y=2^x. try that and u'll see what i mean
21539
If you have a system of equations with two variables of the form ax + by = c, dx + ey = f, where a,b,c,d,e,f are the coefficients, and x and y are variables, you can set up the equation as \n\n[a b][x] = [c]\n[d e][y] = [f]\n\n(ignore the fact there are two equals signs there, they're only there for formatting reasons)\n\nwhere the square brackets are a crude attempt on by behalf to 'draw' matrices and column vectors.\n\nTo solve the system you need to find the inverse of the matrix of the right hand side (assuming it's invertible to begin with), and "right multiply" (that is multiply from the right of each side of the equation) both sides of the equation.\n\nThat should give you:\n\n[1 0][x] = [ inverse of matrix ][c]\n[0 1][y] = [ ........................ ][f] \n\nThen it's just a matter of performing the calculation.\n\n(sorry for the crappy formatting of the post)
1053962
I am assuming this is an "I hate math so I'm gonna complain about its lack of relevance" question and not a real question, but I'll answer it anyway.  I can't tell you every use of it, I suppose I've seen several, but here's one I see a lot.  If you have an object thrown in a trajectory, and you need to know when it will cross a certain height, or when it will be going a certain speed (I dunno, in case you're lobbing hand grenades or missiles someday when you're bored), the quadratic equation will come up in the solution, and it will give you BOTH of the answers, one for when the object is on the way up and one for when it's on the way down.
778614
y =mx + b\n\nFirst, the word linear will tell you this is the answer, as linear graph functions follow this format. From "best expressed", i got the hint that 4) is the answer cos its is the most direct relation. i.e. you plot in x and you get y, like a direct mirror.\n\n1) A quadratic equation will give you 2 solutions to a number you plot in, and from this itself, we can eliminate it. \n2) Complicated. The relationship isnt clear also, cos the entire thing seems to be pure gibberish\n3) This formula can only be applied in a right angled triangle. So it only shows ONE kind of relationship two variables can have.\n\nHope this helps=)