solve each of the following system

Question

1.solve each of the following system.

{y-x=6
{2x^2+y^2=27

Answer 1

Hi Vivian, to solve this set of equations, we can set the y variable equal to x + 6 from the first equation. Then replace the y variable in the second equation with x + 6.

 

This gives:

 

2x² + (x + 6)² = 27

 

2x² + x² + 12x + 36 = 27

 

Combine terms gives:

 

3x² + 12x + 9 = 0

 

Divide all terms by 3 gives:

 

x² + 4x + 3 = 0

 

Factoring gives:

 

(x + 1) * (x + 3) = 0

 

Use the zero product rule to solve:

 

x + 1 = 0, x = -1

 

x + 3 = 0, x = -3

 

When x = -1, y = 5. When x = -3, y = 3.

 

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