Solving these two equations simultaneously:
From the first equation, we can rewrite it as:
x = 6 - y
Substitute x into the second equation:
6−y6 - y6−y^2 - y = 1436 - 12y + y^2 - y = 14y^2 - 13y + 22 = 0
Now we can solve for y by using the quadratic formula:
y = 13±√(132−4<em>1</em>22)13 ± √(13^2 - 4<em>1</em>22)13±√(132−4<em>1</em>22) / 2y = 13±√(169−88)13 ± √(169 - 88)13±√(169−88) / 2y = 13±√8113 ± √8113±√81 / 2y = 13±913 ± 913±9 / 2
So, y = 13+913 + 913+9 / 2 = 11 or y = 13−913 - 913−9 / 2 = 2
Now, substitute the values of y back into x = 6 - y to find the corresponding values of x:
For y = 11:x = 6 - 11 = -5
For y = 2:x = 6 - 2 = 4
Therefore, the solutions to the system of equations are:x = -5, y = 11ORx = 4, y = 2
Solving these two equations simultaneously:
From the first equation, we can rewrite it as:
x = 6 - y
Substitute x into the second equation:
6−y6 - y6−y^2 - y = 14
36 - 12y + y^2 - y = 14
y^2 - 13y + 22 = 0
Now we can solve for y by using the quadratic formula:
y = 13±√(132−4<em>1</em>22)13 ± √(13^2 - 4<em>1</em>22)13±√(132−4<em>1</em>22) / 2
y = 13±√(169−88)13 ± √(169 - 88)13±√(169−88) / 2
y = 13±√8113 ± √8113±√81 / 2
y = 13±913 ± 913±9 / 2
So, y = 13+913 + 913+9 / 2 = 11 or y = 13−913 - 913−9 / 2 = 2
Now, substitute the values of y back into x = 6 - y to find the corresponding values of x:
For y = 11:
x = 6 - 11 = -5
For y = 2:
x = 6 - 2 = 4
Therefore, the solutions to the system of equations are:
x = -5, y = 11
OR
x = 4, y = 2