# Solving Systems of Linear Equations

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Linear equations are the equations in which the highest exponent of the variable is ‘1’. Linear equations consist of variables and constants combined together and we can solve a linear equation to find the value of the variable. A system of linear equations consist of more than one linear equation with different variables and this system can be solved in order to find the value of the variables. System of linear equations can be solved graphically or algebraically using different methods to get the value of the variables.

Example 1: Solve the system of linear equations, x + y = 5 and x – y = 7.

We can solve the given system of equations using the Elimination/Addition method.

Add the given two equations andthen cancel the ‘y’ term.

This gives: 2x= 5+ 7 = 12.

This gives: x = 12/2= 6 ==>x = 6.

Substitute x = 6 in any of the given two equations.

For x+ y = 5==> 6+ y = 5 ==>y = 5 – 6==>y= -1.

Hence the solution: x = 6 and y = -1.

Example 2: Solve the system of linear equations, x + y = 4 and x – y = 2.

We can solve the given system of equations using the Elimination/Addition method.

Add the given two equations and then cancel the ‘y’ term.

This gives: 2x= 4+ 2 = 6.

This gives: x= 6/2= 3 ==>x = 3.

Substitute x= 3 in any of the given two equations.

For x+ y = 4==> 3+ y = 4 ==>y = 4 – 3==>y = 1.

Hence the solution: x = 3 and y = 1.