Linear equation in Math can be defined as expression with highest degree of variable in equation equals to one. System of Linear Equations can be solved by adding or subtracting the equation and getting values of unknown variables. Number of equations we need to solve for 'n' number of variable in linear equations is equals to 'n'. General representation of linear equation is given as follows:
PY = QMX + D
Where, P and Q are the coefficients of terms Y and X respectively. 'M' denotes Slope of line and D denotes Y – intercept. When solving linear equations, how to bring a fraction to the other side linear equation?
For this let us suppose an example of a linear equation given in variable 'X' as follows:
P X+ Q = R X + Z,
Where, P. Q. R and Z are constants.
To solve this equation, we first have to bring unknown quantities on one side and known quantities like constants to other side of equation. In our example we do it like this:
X (P – R) = Z – Q,
Or X = (Z – Q) / (P – R),
For example, if linear equation is given as follows: 2 x + 5 = 4x – 9,
This equation can be solved using the above method and substituting the values of P, Q, R and Z to get X as:
X = (-9 – 5) / (2 – 4) = 7,
For example, if we have an equation given as: 16 (X + 2) = −20. We solve it as follows:
X + 2 = -20 / 16,
Or X = (-20 / 16) – 2,
Or X = (-20 - 32) / 16 = -52 / 16 = -13 / 4.