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

July 25, 2021 | education

| 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.