A system of equations is shown.

Question

1
y = x
2
1
y = – x + 2
2
Kayla graphs the system to solve it. She marks her solutions with P and R.
y
5
4
3
2 P
1 –5 –4–3–2–1 0 –1 R1 2 3 4 –2 –3 –4 –5
x
5

This question has two parts.
Part A
Which statement describes Kayla’s solutions?
A Her solutions are correct.
B She marked the y-intercepts instead of the x-intercepts.
C She marked the y-intercepts instead of the intersection point of the
two lines.
D She marked only the y-intercepts instead of the x- and y-intercepts.
Part B
What is a solution to the system of equations?
Write your responses in the shaded boxes below.

Answer 1

To analyze the given equations:

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

Part A: Evaluating the Statements

To determine the right statement about Kayla’s solutions, we need to find the intersection point of these two lines.

1. Start by setting the equations equal to each other to find the point where they intersect: \[ x = -x + 2 \]

2. Combine like terms: \[ x + x = 2 \implies 2x = 2 \implies x = 1 \]

3. Substitute \(x = 1\) back into either equation to find \(y\):

   • Using \(y = x\): \[ y = 1 \]

So the intersection point, which is the solution to the system of equations, is \((1, 1)\).

If Kayla marked points P and R on her graph, we need to compare these points with the intersection point \((1, 1)\):

• If P or R is at \((1, 1)\), then her solutions are correct.
• If P or R are at the y-intercepts (like \((0, 0)\) for \(y = x\) and \((0, 2)\) for \(y = -x + 2\)), she marked the wrong points.

Without the specific coordinates of points P and R, the best choice would depend on what those coordinates are (which we are not provided).

Assuming P and R do not match \((1, 1)\), then the correct choice would be:

• C: She marked the y-intercepts instead of the intersection point of the two lines.

Part B: Solution to the System of Equations

The solution to the system is \((1, 1)\).

Here is how you would write it in the shaded box:

• Answer: \( (1, 1) \)

If you need to input a different format, please clarify!