Question

Look at these two equations.

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

Yes

No

Answer 1

To determine if there is an ordered pair that is a solution to both equations, we need to find a point where the two lines intersect.

The equations are:
1. \( y = x + 1 \)
2. \( y = -x + 5 \)

We can set them equal to each other to find the intersection:

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

Now, combine like terms:

\[
x + x = 5 - 1
\]
\[
2x = 4
\]
\[
x = 2
\]

Now, substitute \( x = 2 \) back into one of the original equations to find \( y \):

Using \( y = x + 1 \):
\[
y = 2 + 1 = 3
\]

So, the ordered pair is \( (2, 3) \).

To confirm, we can check this ordered pair in the second equation:

Using \( y = -x + 5 \):
\[
y = -2 + 5 = 3
\]

Since \( (2, 3) \) satisfies both equations, the answer is:

**Yes**, there is an ordered pair \((2, 3)\) that is a solution to both equations.