(- 1, - 4)
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Given system:
We see two variables (x and y) and one of them (y) is of first degree in both equations.
The most suitable method is to isolate y and substitute.
See how to do so below:
- 2x² + 4x + y = -6 ⇒ y = - 2x² - 4x - 6
- x² + 2x - y = 3 ⇒ y = x² + 2x - 3
Equate RHS of the two equations and solve for x:
- - 2x² - 4x - 6 = x² + 2x - 3
- x² + 2x² + 2x + 4x - 3 + 6 = 0
- 3x² + 6x + 3 = 0
- x² + 2x + 1 = 0
- (x + 1)² = 0
- x + 1 = 0
- x = - 1
Find the value of y by substituting the value of x back to one of equations;
- y = (-1)² + 2(- 1) - 3
- y = 1 - 2 - 3
- y = - 4
So the solution is (- 1, - 4).
Note:
Alternative method would be graphing. By plotting two parabolas find the intersection of graphs to give you solution:
- f(x) = - 2x² - 4x - 6
- g(x) = x² + 2x - 3