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
yes or no

Answer 1

To determine if there is an ordered pair that is a solution to both equations, we need to analyze them.

The first equation is:
\( y = x + 1 \)

The second equation provided seems to have a typo. I assume you meant \( y = -x + 5 \).

Let's set both equations equal to see if there's a point of intersection:

1. From the first equation, we have:
\( y = x + 1 \)

2. From the second equation, correcting it to:
\( y = -x + 5 \)

Now we set them equal to each other to find the intersection:
\( x + 1 = -x + 5 \)

Now, 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 substitute \( x = 2 \) back into the first equation to find \( y \):
\( y = 2 + 1 = 3 \)

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

So the answer is **yes**, there is an ordered pair that satisfies both equations.