how many solutions does this linear system have? y = 2x - 5 -8x - 4y = -20 one solution: (-2.5, 0) one…

Explanation:

Step1: Rewrite the second - equation

Transform $-8x - 4y=-20$ into slope - intercept form $y=mx + b$. First, isolate $y$: $-4y=8x - 20$, then $y=-2x + 5$.

Step2: Analyze the relationship between the two equations

The first equation is $y = 2x-5$, and the second is $y=-2x + 5$. The slopes of the two lines are $m_1 = 2$ and $m_2=-2$, which are different. Two lines with different slopes in a two - dimensional plane intersect at exactly one point.

Answer:

one solution: $(2.5,0)$ (Substitute $y = 0$ into $y = 2x-5$, we get $0=2x - 5$, then $2x=5$, $x = 2.5$)