$$ y=x+2 $$ and $$ x+x y=4 $$ sub (1) into

Question

UpStudy AI · Accepted Answer

We start with the given equations:

(1) y = x + 2  
  (2) x + x·y = 4

Substitute equation (1) into (2) by replacing y with (x + 2):

x + x(x + 2) = 4

Now, simplify the equation:

x + x² + 2x = 4  
  x² + 3x = 4

Subtract 4 from both sides to set the equation to 0:

x² + 3x − 4 = 0

Next, solve the quadratic equation x² + 3x − 4 = 0. We can use the quadratic formula:

x = [−b ± √(b² − 4ac)] / (2a)

Here, a = 1, b = 3, and c = −4. Compute the discriminant:

b² − 4ac = 3² − 4(1)(−4) = 9 + 16 = 25

Then,

x = [−3 ± √25] / 2  
  x = [−3 ± 5] / 2

This gives two solutions:

x = (−3 + 5) / 2 = 2 / 2 = 1  
  x = (−3 − 5) / 2 = (−8) / 2 = −4

Now, substitute each value of x back into equation (1) to find y.

For x = 1:
  y = 1 + 2 = 3

For x = −4:
  y = −4 + 2 = −2

Thus, the solutions to the system of equations are:

(x, y) = (1, 3) and (x, y) = (−4, −2).
The solutions are (1, 3) and (−4, −2).

\( y=x+2 \) and \( x+x y=4 \) sub (1) into