To solve a system of linear equations (two variables (x) and (y)), we can use the substitution or elimination method. Below is a step-by-step example with a common problem:

Example Problem

Solve:

1. (3x - y = 7)
2. (5x + 2y = 19)

Step 1: Use Substitution

From equation 1, solve for (y):
(y = 3x - 7)

Step 2: Substitute (y) into Equation 2

Replace (y) in equation 2 with (3x -7):
(5x + 2(3x -7) = 19)

Simplify:
(5x +6x -14 =19)
(11x = 33)
(x = 3)

Step 3: Find (y)

Substitute (x=3) into (y=3x-7):
(y =3(3)-7 =9-7=2)

Final Solution: (x=3), (y=2)

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