The solutions of the nonlinear system of equations are the points (x₁, y₁) = (- 2, 10) and (x₂, y₂) = (3, 5).
How to solve a system of algebraic equations
We find in this place a non-linear system formed by a quadratic equation and a linear equation, which can be solved by algebra properties. The complete procedure is shown below:
y = 2 · x² - 3 · x - 4 (1)
y + x = 8 (2)
By (2) in (1):
2 · x² - 3 · x - 4 + x = 8
2 · x² - 2 · x - 12 = 0
2 · (x² - x - 6) = 0
2 · (x - 3) · (x + 2) = 0
x = 3 ∨ x = - 2
y = 8 - 3 ∨ y = 8 - (- 2)
y = 5 ∨ y = 10
The solutions of the nonlinear system of equations are the points (x₁, y₁) = (- 2, 10) and (x₂, y₂) = (3, 5).
To learn more on quadratic equations: https://brainly.com/question/17177510
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