How do I solve linear system questions and give an example?

 𝙰𝙽𝚂𝚆𝙴𝚁 = To solve a linear system of equations, you need to find the values of the variables that satisfy all of the equations in the system. There are several methods for solving linear systems, including substitution, elimination, and matrices.

Here is an example of how to solve a linear system using the substitution method:

Example: Solve the system of equations:

2x + y = 7
x - y = 1
  1. Solve for one variable in terms of the other in one of the equations. Let's solve for y in the second equation:
makefile
x - y = 1
y = x - 1
  1. Substitute this expression for y into the other equation and solve for x. Let's substitute y = x - 1 into the first equation:
makefile
2x + y = 7
2x + (x - 1) = 7
3x - 1 = 7
3x = 8
x = 8/3
  1. Substitute the value of x back into one of the equations to solve for y. Let's use the second equation:
makefile
x - y = 1
8/3 - y = 1
y = 5/3

Therefore, the solution to the system of equations is x = 8/3 and y = 5/3.

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