To solve this system of equations, we can start by isolating x in the first equation:
x = 7 + u
Next, we substitute this expression for x into the second equation:
(7 + u)^2 + u^2 = 9 - 2(7)(u)
Expanding and simplifying, we get:
49 + 14u + u^2 + u^2 = 9 - 14u
Combining like terms, we have:
2u^2 + 14u - 40 = 0
Dividing by 2 to simplify, we get:
u^2 + 7u - 20 = 0
Now, we can factorize this quadratic equation:
(u + 10)(u - 2) = 0
Setting each factor to zero, we solve for u:
u + 10 = 0 or u - 2 = 0u = -10 or u = 2
Now that we have the values of u, we can find the corresponding values of x by using x = 7 + u:
If u = -10:x = 7 - 10 = -3
If u = 2:x = 7 + 2 = 9
Therefore, the solutions to the system of equations are:x = -3, u = -10x = 9, u = 2
To solve this system of equations, we can start by isolating x in the first equation:
x = 7 + u
Next, we substitute this expression for x into the second equation:
(7 + u)^2 + u^2 = 9 - 2(7)(u)
Expanding and simplifying, we get:
49 + 14u + u^2 + u^2 = 9 - 14u
Combining like terms, we have:
2u^2 + 14u - 40 = 0
Dividing by 2 to simplify, we get:
u^2 + 7u - 20 = 0
Now, we can factorize this quadratic equation:
(u + 10)(u - 2) = 0
Setting each factor to zero, we solve for u:
u + 10 = 0 or u - 2 = 0
u = -10 or u = 2
Now that we have the values of u, we can find the corresponding values of x by using x = 7 + u:
If u = -10:
x = 7 - 10 = -3
If u = 2:
x = 7 + 2 = 9
Therefore, the solutions to the system of equations are:
x = -3, u = -10
x = 9, u = 2