Solving System of Equations

In mathematics, a system of linear equations is a collection of linear equations involving the same set of variables. For example,

is a system of three equations in the three variables . A solution to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by

since it makes all three equations valid.so this is specially for linear equations in two variables or more than two variables.

In mathematics, the theory of linear systems is a branch of linear algebra, a subject which is fundamental to modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and such methods play a prominent role in engineering, physics, chemistry, computer science, and economics. A system of non-linear equations can often be approximated by a linear system (see linearization), a helpful technique when making a mathematical model or computer simulation of a relatively complex system.This is how linear equations explained ,let's see a example on this now from linear algebra tutoring online.
Question:-

Solve the system of equations

8x-z=4

y+z=5

11x+y=15

Answer:-

8x-z=4 ----- eq1

y+z=5 ---- eq2

11x+y=15 -----eq3

add eq1 and eq2

we get 8x+y=9 ----- eq4

subtract eq4 from eq3

11x+y=15
-8x+y=9
-----------
3x = 6

x =2

putting this value in eq1

8x-z =4

16-z=4

z=12

putting this value in eq2

y+z = 5

y = -7

so x=2 , y= -7 and z=12

Converting an algebraic expression into dependent variables of a single variable

Here is an algebra question where in a given algebraic expression like terms are on one side and unlike term on another side, this problem is all about making into different subject.

Topic : Making into different subject

This example would clearly explain what making into different subject exactly mean.

Problem : Let f = uv / (u + v) Make “v” as the subject

Solution :

f = uv / (u + v)
Multiplying by (u + v) on either sides of the equation
f (u + v) = uv
fu + fv = uv
Subtract fv on both the sides
fu = uv – fv
fu = v(u – f)
fu / (u – f) = v

Hope the meaning on coverting to different subject is well understood by above example, for more algebra questions like this contact algebra help.