Unlock the Code to Solve Linear Simultaneous Equations

Linear simultaneous equations are a set of equations that contain only linear terms (no exponents or other non-linear functions) and are solved simultaneously. These equations usually involve two or more unknown variables.

Substitution Method:

To solve a system of linear equations using the substitution method, we need to solve one of the equations for one of the variables in terms of the other variable. Then, we substitute this expression into the other equation and solve for the remaining variable.

Example:

Solve the following system of linear equations using the substitution method:

x + y = 12
x - y = 2

Solution:
From the first equation, we get x = 12 - y. We can substitute this expression for x in the second equation:
12 - y - y = 2
-2y = -10
y = 5

Now we can substitute this value for y in either of the two original equations to find x:
x + 5 = 12
x = 7

Therefore, the solution to the system is x = 7 and y = 5.

Elimination Method:

The elimination method involves adding or subtracting equations to eliminate one variable. Here's an example to illustrate the elimination method:

Example:

Solve the following system of linear equations using the substitution method:

x + y = 12
x - y = 2

Solution:
We have to eliminate one of the variable to get the value of other one. 
Adding two equations we get,

x + y + x - y = 12 + 2
2x = 14
x = 7

Now we can put this value for x in either of the two original equations to find y:

7 + y = 12
y = 5

Therefore, the solution to the system is x = 7 and y = 5.

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