Simultaneous Equations Problems

Introduction of simultaneous equations problems:

The equations have only one variable whose power is1called a simple equations. A linear equations problems have one variable is of the form Ax + B=0. A linear equations involving two variables is of the form Ax +By +C =0. Here x and y are variables and A, B, C are constants from their problems.

When two linear equations in two variables are satisfied by the same pair of values of the variables, the equations are called simultaneous linear equations. There are different methods for solving simultaneous equation problems.

Methods for Solving Simultaneous Equations Problems:

Type 1: Elimination Method.

Type 2: Substitution Method.

Type 3: Graphing Method.

These are the methods for solving equation used through the problems.

Elimination method:

x+y=5

x-y=10

Solve for x and y

These equations are already in simplified form

So we can directly add them

Since one of the equation have positive y and the another have negative y, so both of them will cancel out and we will get x.

x+y=5

x-y=10

---------

2x = 15

x=15/2

x=7.5

Now plug in the value of x in any of the equation so that we can get the value of y

7.5+y=5

y=5-7.5

y=-2.5

So the value of x is 7.5 and the value of y is -2.5

Simultaneous Equations Problems Substitution Method:

Substitution method:

2x+3y=6

x+y=5

Solve for x and y

Since it is substitution method find any one variable from any of the equation and plug in the other equation.

Here second equation is in simplified form so find x from that

x+y=5

x=5-y

Now plug in the value of x in first equation

So, 2(5-y) +3y=6

10-2y+3y=6

10+y=6

y=6-10

y=-4

Now plug in the value of x in second equation

So, x+y=5

x-4=5

x=5+4

x=9

So the value of x is 9 and the value of y is -4

Both of the methods are simpler and easier for solving simultaneous equation problems.

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Simultaneous Equations Problems Graphical Method:

Find the solution of the simultaneous equations using graphical method: x-y=0, and y=2x-1

We sketch both the straight lines and find the point of intersection of the two lines. Here the lines intersect at (1,1).

That is the solution of the given simultaneous equations is x=1, and y=1

by: Omkar Nayak

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