Question

Solve the system of equations.

x+y=6


x−y=4


(1 point)
The solution is
,
.

Answer 1

To solve the system of equations:

1. \( x + y = 6 \)
2. \( x - y = 4 \)

We can solve this system using the method of substitution or elimination. Here, I will use elimination:

First, we can add the two equations to eliminate \( y \):

\[
(x + y) + (x - y) = 6 + 4
\]

This simplifies to:

\[
2x = 10
\]

Now, divide both sides by 2:

\[
x = 5
\]

Now that we have \( x \), we can substitute it back into one of the original equations to find \( y \). We'll use the first equation:

\[
5 + y = 6
\]

Subtract 5 from both sides:

\[
y = 1
\]

So the solution to the system of equations is:

\( x = 5 \) and \( y = 1 \).

The solution is \( (5, 1) \).