Question

solve.
\

$$\begin{cases} m + n = 5 \\\\ m - n = 3 \\end{cases}$$

use the substitution method.
\bigcirc the solution is (2, -1).
\bigcirc there is no solution.
\bigcirc the solution is (4, 1).
\bigcirc there are an infinite number of solutions.

Explanation:

Step1: Isolate $m$ from first equation

From $m + n = 5$, we get $m = 5 - n$.

Step2: Substitute $m$ into second equation

Substitute $m = 5 - n$ into $m - n = 3$:
$$(5 - n) - n = 3$$
Simplify: $5 - 2n = 3$

Step3: Solve for $n$

Rearrange to solve for $n$:
$-2n = 3 - 5$
$-2n = -2$
$n = \frac{-2}{-2} = 1$

Step4: Substitute $n$ to find $m$

Substitute $n = 1$ into $m = 5 - n$:
$m = 5 - 1 = 4$

Answer:

The solution is (4, 1).