Question

The system on the left can be reduced to:

tu=99, t−9u=−9
Solving the system, t = _______, u = _______.

Answer 1

To solve the given system of equations, we can use the method of substitution. After rearranging the second equation and substituting the value of t into the first equation, we end up with a quadratic equation. Solving this quadratic equation gives us the solutions t = 18, u = 3 and t = -45, u = -4.

Step-by-step explanation:

The given equations are:

• tu=99
• t−9u=−9

To solve this system of equations, we can use the method of substitution. We can rearrange the second equation to solve for t as t = 9u - 9. Then substitute this value of t into the first equation:

(9u - 9)u = 99

Expanding and rearranging the equation, we get:

9u^2 - 9u - 99 = 0

Factoring out a 9, we have:

9(u^2 - u - 11) = 0

Solving for u using the quadratic formula gives two solutions: u = 3 and u = -4. Substitute these values back into the equation t = 9u - 9 to find the corresponding values of t: t = 18 and t = -45.

Therefore, the solutions to the system of equations are t = 18, u = 3 and t = -45, u = -4.