How can x² + 3x + 1 = 2x² + 2x + 3 be set up as a system of equations?

Solution:

Let us set the given equations equal to y.

x² + 3x + 1 = 2x² + 2x + 3

⇒ y = x² + 3x + 1

⇒ y = 2x² + 2x + 3.

Solving the above equation.

x² + 3x + 1 = 2x² + 2x + 3

Subtract x² from both sides.

3x + 1 = x² + 2x + 3.

Subtract 3x from both sides.

1 = x² - x + 3

Subtract 1 from both sides.

x² - x + 2 = 0

Using the quadratic formula to solve this,

x =[-b ± √(b)² - 4ac]/ 2a

x = [-(-1) ± √(- 1)² - 4 × 1 × 2]/ 2(1)

x = [1 ± √1 - 8 ]/ 2

x = [1 ± √-7 ]/ 2

x = [1 ± i√7]/ 2

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How can x² + 3x + 1 = 2x² + 2x + 3 be set up as a system of equations?

Summary:

The expression x² + 3x + 1 = 2x² + 2x + 3 can be set up as system of equations as y = x² + 3x + 1 and y = 2x² + 2x + 3.