Solve the following system. y = (1 / 2)x² + 2x - 1 and 3x - y = 1

Solution:

Given, y = (1 / 2)x² + 2x - 1 ------------------ (1)

3x - y = 1 ------------ (2)

Using substitution method,

Put the value of y in equation (2), we get

3x - [(1 / 2)x² + 2x - 1] = 1

3x - (1 / 2)x² - 2x + 1 = 1

Grouping of common terms,

3x - 2x - (1/2)x² = 0

x - (1/2)x² = 0

2x - x² = 0

Taking out common term,

x(2 - x) = 0

x = 0 

Also, (2 - x) = 0

x = 2

Now, put x = 2 in (2)

3(2) - y = 1

6 - y = 1

y = 5

Therefore, the solution is (2,5)

---

Solve the following system. y = (1 / 2)x² + 2x - 1 and 3x - y = 1

Summary:

The solution to the system of equation y = (1 / 2)x² + 2x - 1 and 3x - y = 1 is (2,5)