Question

what is the solution to this system of linear equations?
x + y = 4
x - y = 6
(4, 6)
(6, 4)
(5, -1)
(-1, 5)

Explanation:

Step1: Add the two equations

To eliminate \( y \), we add the equations \( x + y = 4 \) and \( x - y = 6 \).
\[

$$\begin{align*} (x + y) + (x - y) &= 4 + 6\\ x + y + x - y &= 10\\ 2x &= 10 \end{align*}$$

\]

Step2: Solve for \( x \)

Divide both sides of \( 2x = 10 \) by 2.
\[
x = \frac{10}{2} = 5
\]

Step3: Substitute \( x = 5 \) into the first equation

Substitute \( x = 5 \) into \( x + y = 4 \).
\[
5 + y = 4
\]

Step4: Solve for \( y \)

Subtract 5 from both sides of \( 5 + y = 4 \).
\[
y = 4 - 5 = -1
\]

Answer:

\((5, -1)\)