Question

Is there an ordered pair that is a solution to BOTH of these linear equations? *You can type them into the Desmos calculator to see the graph. y=x+1 y=−x+5

Answer 1

To determine if there is an ordered pair that is a solution to both equations, we can find the point where the two lines \( y = x + 1 \) and \( y = -x + 5 \) intersect.

We can set the two equations equal to each other to find the \( x \) value at the intersection:

\[
x + 1 = -x + 5
\]

Now, let's solve for \( x \):

1. Add \( x \) to both sides:
\[
2x + 1 = 5
\]

2. Subtract 1 from both sides:
\[
2x = 4
\]

3. Divide by 2:
\[
x = 2
\]

Now that we have \( x = 2 \), we can substitute it back into either equation to find the corresponding \( y \) value. We'll use the first equation:

\[
y = x + 1 = 2 + 1 = 3
\]

So, the ordered pair (solution to both equations) is:

\[
(2, 3)
\]

You can verify this by plugging \( x = 2 \) into the second equation as well:

\[
y = -x + 5 = -2 + 5 = 3
\]

Thus, the ordered pair \( (2, 3) \) is indeed a solution to both equations.