in an equation like y=5x+3 the 3 would be the y-intercept
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== Linear equations are those that use only linear functions and operations. Examples of linearity: differentiation, integration, addition, subtraction, logarithms, multiplication or division by a constant, etc. Examples of non-linearity: trigonometric functions (sin, cos, tan, etc.), multiplication or division by variables.
It means that at least one of the equations can be expressed as a linear combination of some of the other equations. A linear combination of equations is the addition (or subtraction) of equations. And since an equation can be added several times, it includes multiples of equations. For example, if you have x + 2y = 3 and 2x + y = 4 Then adding 2 times the first and 3 times the second gives 8x + 7y = 18 This is, therefore, dependent on the other 2. If you have n unknown variables, there will be a unique solution if, and only if, you must have a set of n independent linear equations.
Equations are not linear when they are quadratic equations which are graphed in the form of a parabola
Lety be the column vector the dependent variable,M be the matrix of coefficients, andx be the column vector of variablesso that the system of equations may be represented by y = Mx.Then the solution set is obtained by left-multiplying both sides by M^-1that is x = M^-1*y
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.