Question

systems of linear equations lesson 3 one solution, no solution, or many solutions does the graph show the system of equations $x + y = 2$ and $-x + y = 7$? should the lines for the system be parallel? (1 point) \bigcirc the graph of $-x + y = 7$ is incorrect. the lines should be parallel. \bigcirc the graph of $-x + y = 7$ is incorrect. the lines should intersect. \bigcirc both graphs are correct. the lines should be parallel.

Explanation:

Step1: Analyze slopes of equations

For \(x + y = 2\), rewrite as \(y=-x + 2\), slope \(m_1=-1\).
For \(-x + y = 7\), rewrite as \(y=x + 7\), slope \(m_2 = 1\).

Step2: Determine parallelism

Parallel lines have equal slopes. Here, \(m_1
eq m_2\), so lines should intersect (not parallel).

Step3: Evaluate graph accuracy

The dashed line (supposed to be \(-x + y = 7\)) has slope (from points like \((0, -7)\) and, say, \((3, -10)\)): \(\frac{-10 - (-7)}{3 - 0}=\frac{-3}{3}=-1\), which is wrong (should be \(1\)). So its graph is incorrect, and lines should intersect (since slopes differ).

Answer:

The graph of \(-x + y = 7\) is incorrect. The lines should intersect.