Simultaneous equations

Simultaneous Equations: If two unknown values had to be solved at the same time then these type of equations are called Simultaneous Equations. Simultaneous forms of equations are two equations with two unknowns. They are called simultaneous because they must both be solved at the same time.

There are various methods to solve Simultaneous-equations.
Simultaneous Equation solver:
How to Solve Simultaneous Equations: These equations can be solved by  by elimination method,  Solving by substation method  and by squaring method.  These equations can also be solved by graphing.

Solving Simultaneous equations.

In the  elimination   method for solving  equations, two equations are simplified by adding them or subtracting them. This eliminates one of the variables so that the other variable can be found.
To add two equations, add the left hand expressions and right hand expressions separately. Similarly, to subtract two equations, subtract the left hand expressions from each other, and subtract the right hand expressions from each other.

Take for example two equations.  x +y=10 and x-y = 2.
See  if by adding or subtracting one variable can be  eliminated. When we add these two equations  +y and –y gets cancelled.
we get 2x =12.

Hence  x = 6  Now plug in the value of x in any one equation say x + y=10
We get 6+y=10, so y = 10-6 which equals 4.  So the solution is  x =6 and  y=4

To solve by substitution , we take one of the equations and solve for x in terms of y  or solve for y in terms of x  Then this value is substituted in the unknown equation and solved for the next variable.
For example  x = 8-y and  2x – y  =  7.
Substitute 8-y  for x in the  2x – y = 7  and solve for y.
2(8-y) - y=7 . now  distribute it.
16 – 2y -y = 7  which equals 16 – 3y  = 7.
We have -3y = -9  Hence  y = 3 .

To find  x, put  value of  y  in the equation 2x – y =7.  We get  2x -3 = 7   so 2x = 10 and x = 5

To solve by graphing bring the two equations to the   y = mx + b form  where m is the slope and b is the y intercept.  Using this first mark the  y  intercept and the slope points.  Plot the points and draw  a straight line connecting  the dots .  Note the point where the two  lines intersects  one another.  From this point of intersection of the lines we can be found the values of  x and y.