# First Order Equations With Two Variables Calculator

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The First Order Equations With Two Variables Calculator will calculate:

1. The solution (root) of first-order equations with two variables.
 🖹 Normal View🗖 Full Page View Calculator Precision (Decimal Places)0123456789101112131415 Coefficient (a) Coefficient (b) Constant (c) Independent variable (x)
Dependent variable Formula and Calculations Dependent variable (y) = / Slope (k) = Constant (n) = y = -a/bx - c/b y = -/ - / y = -/ - / y = / k = -a/b k = -/ k = n = -c/b n = -/ n = Coefficient (a) = Coefficient (b) = Constant (c) = Independent variable (x) =

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each first order equations with two variables calculation, the First Order Equations With Two Variables Calculator will automatically calculate the results and update the formula elements with each element of the first order equations with two variables calculation. You can then email or print this first order equations with two variables calculation as required for later use.

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Please provide a rating, it takes seconds and helps us to keep this resource free for all to use ## Theoretical description

An equation is a mathematical statement consisting of an equal symbol between two algebraic expressions (open sentences) that have the same value. When combined, these two equal open sentences form a single closed sentence. The difference between closed sentences and equations is that closed sentences may be either true or false while equations are supposed to be always true.

Like in algebraic expressions, every equation contains variables, coefficients and constants.

Variables are unknown numbers expressed by means of letters, for example, x, y, z, a, b, c, m, n, etc. The ultimate goal when dealing with an equation is to calculate the value of its variables.

Coefficients are numbers that multiply (or divide) variables and that precede them. It is a norm that if during calculations a coefficient appears after the variable, the equation is rearranged so that all coefficient precede their corresponding variable.

For example, in the equation 3x - 2y = 6, we have two coefficients: 3 and -2 and they are followed by their corresponding variables: namely x and y.

Constants are "free" numbers that are not associated with any variable. They usually appear after the equal sign (giving the value of the equation), but we may see constants appearing in the side that contains variables as well, especially in the original form of equations (before making any operation). In the above equation, the constant is 6.

Any part of the equation containing the product of a coefficient and one or more variables (they may also be in a certain power) is called a term. Equation terms are separated from each other by 'plus' or 'minus' symbols. This means addition and subtraction act as separators of any equation terms, which on the other hand bear the sign preceding them. In addition, the constant also represents a separate term in an equation.

Solving a first-order equation with two variables means calculating the value of its dependent variable by giving values to the independent variable. In math language, this process is called "finding the root of the equation".

The first-order equation with two variables - otherwise known as a linear equation - contains two variables (usually denoted as x and y), two coefficients (a and b) and a constant c, The general form of first-order equations with two variables is

ax + by + c = 0

Usually, one of the variables (usually x) is independent (we give values to it), so you can find the value of the other variable (the dependent one, usually y) in terms of the independent variable. In this way, the first-order equation with two variables turns into a first-order equation with one variable.

The necessary thing to do when solving such equations is to isolate the dependent variable (for example y). Thus, we have

ax + by + c = 0
by = -ax - c

Dividing both sides by b yields

by/b = -ax/b - c/b
y = -a/bx - c/b

This is a new (simplified) form of a linear equation representation of the type

y = mx + n

where the coefficient m (often denoted as k) represents the gradient (slope) of the equation's graph.

For example, in the equation 3x - 5y + 7 = 0, we have a = 3 and b = -5 and c = 7. Thus,

k = -a/b
= -3/-5
= 3/5

Likewise, the constant n is

n = k = -c/b
= -7/-5
= 7/5

Therefore, the equation can be also written as

y = 3/5x + 7/5

If you give a value to the independent variable x (for example x = 10) you obtain the corresponding value for the dependent variable y. Here, we have

y = 3/5 ∙ 10 + 7/5
= 30/5 + 7/5
= 37/5

Indeed, substituting these two values in the original equation yields

3x - 5y + 7 = 0
3 ∙ 10 - 5 ∙ 37/5 + 7 = 0
30 - 37 + 7 = 0
0 = 0 (true)

## Equations Math Tutorials associated with the First Order Equations With Two Variables Calculator

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