Question

Solve the system using any method. Select all that apply.

2x² + 4x + y = -6
x² + 2x - y = 3

Explain your choice of method.

Answer 1

(- 1, - 4)

=============

Given system:

• 2x² + 4x + y = -6

• x² + 2x - y = 3

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