An equation that is true for some value(s) of the variable(s) and not true for others. Example: The equation 2x – 5 = 9 is conditional because it is only true for x = 7. Other values of x do not satisfy the equation.
The pair of linear equations have three conditions, If a1/a2 ≠ b1/b2 the pair of linear equations is consistent. If a1/a2 = b1/b2 ≠ c1/c2 the pair of linear equations is inconsistent. If a1/a2 = b1/b2 = c1/c2 the pair of linear equations is dependent and consistent.
Representation of Pair Of Linear Equation In Two Variables If the pair of linear equations is consistent, then: a1/a2 ≠ b1/b. If the pair of linear equations is inconsistent, then: a1/a2 = b1/b2 ≠ c1/c. If the pair of linear equations is dependent and consistent, then: a1/a2 = b1/b2 = c1/c.
A linear equation in one variable is an equation which has a maximum of one variable of order 1. It is of the form ax + b = 0, where x is the variable. This equation has only one solution.
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.
If a, b, and r are real numbers (and if a and b are not both equal to 0) then ax+by = r is called a linear equation in two variables. (The “two variables” are the x and the y.) The numbers a and b are called the coefficients of the equation ax+by = r. The number r is called the constant of the equation ax + by = r.
The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
A linear function must satisfy f(cx)=cf(x) for any number c. The other requirement for a linear function is that applying f to the sum of two inputs x and y is the same thing as adding the results from being applied to the inputs individually, i.e., f(x+y)=f(x)+f(y).
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.
The standard form of linear equations in one variable is expressed as Ax + B = 0, where x is the single variable and A and B are integers. For example, 6x + 7 = 18 is a linear equation in one variable which is written in its standard form.