Question

solve the system by the addition method.$x+y = 4$$x-y = 6$select the correct choice below and fill in any answer boxes present in your choice.a. the solution set is {}. (simplify your answer. type an ordered pair.)b. there are infinitely many solutions.c. there is no solution.

Explanation:

Step1: Add the two equations

$$(x + y) + (x - y) = 4 + 6$$
$$2x = 10$$

Step2: Solve for x

$$x = \frac{10}{2} = 5$$

Step3: Substitute x into first equation

$$5 + y = 4$$

Step4: Solve for y

$$y = 4 - 5 = -1$$

Answer:

A. The solution set is $\{(5, -1)\}$. (Simplify your answer. Type an ordered pair.)