Question

which graph represents this system?
2x - 5y = -5
y = \frac{2}{5}x + 1

Explanation:

Step1: Rewrite the first equation

Let's rewrite \(2x - 5y=-5\) in slope - intercept form (\(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept).
Start with \(2x-5y=-5\). Subtract \(2x\) from both sides: \(-5y=-2x - 5\).
Then divide each term by \(-5\): \(y=\frac{-2x}{-5}+\frac{-5}{-5}\), which simplifies to \(y = \frac{2}{5}x+1\).

Step2: Compare the two equations

The second equation is already in slope - intercept form: \(y=\frac{2}{5}x + 1\).
We can see that both equations have the same slope (\(m=\frac{2}{5}\)) and the same y - intercept (\(b = 1\)). This means that the two lines are coincident (they are the same line). So the graph that represents this system is a single line (since the two equations represent the same line).

Answer:

The two equations represent the same line, so the graph is a single line with slope \(\frac{2}{5}\) and y - intercept \(1\) (any graph showing a single line corresponding to \(y=\frac{2}{5}x + 1\) represents this system).