Solution of systems of linear equations by the substitution method {y-2x = 3 {2x + 3y = 1.

1. Let us express y from the first equation in terms of x:
y – 2 x = 3,
y = 3 + 2 x.
2. Substitute the value of y into the second equation and define x:
2 x + 3 y = 1,
2 x + 3 (3 + 2 x) = 1,
2 x + 9 + 6 x = 1,
8 x = 1 – 9,
8 x = -8,
x = -8: 8,
x = -1.
3. Let’s calculate the value of y:
y = 3 + 2 x = 3 + 2 (-1) = 3 – 2 = 1.
4. Verification:
y – 2 x = 1 – 2 (-1) = 1 + 2 = 3,
2 x + 3 y = 2 (-1) + 3 1 = -2 + 3 = 1.
Answer: x = -1, y = 1.