Question

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a system of equations is given. write each linear equation in slope - intercept form. then describe the graph of the system, and give the number of solutions.
5x - y = 9
-4y = -20x + 36
part 1 of 3
the slope - intercept form of the equation 5x - y = 9 is
the slope - intercept form of the equation -4y = -20x + 36 is

Explanation:

Step1: Isolate y for first equation

Start with $5x - y = 9$. Subtract $5x$ from both sides, then multiply by -1:
$-y = -5x + 9$
$y = 5x - 9$

Step2: Isolate y for second equation

Start with $-4y = -20x + 36$. Divide all terms by -4:
$y = \frac{-20x}{-4} + \frac{36}{-4}$
$y = 5x - 9$

Step3: Analyze the system

Both equations simplify to the same line, so they are coinciding lines. Coinciding lines have infinitely many overlapping points, meaning infinitely many solutions.

Answer:

1. Slope-intercept form of $5x - y = 9$: $y = 5x - 9$
2. Slope-intercept form of $-4y = -20x + 36$: $y = 5x - 9$
3. The graph consists of two coinciding (identical) lines, and the system has infinitely many solutions.