Questions: System A Line 1: y=-5/2 x-3 Line 2: 5 x+2 y=-6 This system of equations is: consistent dependent consistent independent inconsistent This means the system has: a unique solution no solution infinitely many solutions

System A
Line 1: y=-5/2 x-3

Line 2: 5 x+2 y=-6

This system of equations is:
consistent dependent consistent independent inconsistent

This means the system has:
a unique solution
no solution
infinitely many solutions

Transcript text: System A Line 1: $y=-\frac{5}{2} x-3$ Line 2: $5 x+2 y=-6$ This system of equations is: consistent dependent consistent independent inconsistent This means the system has: a unique solution no solution infinitely many solutions

Solution

Solution Steps

Step 1: Identify the equations

The given system of equations is:

$ y = -\frac{5}{2}x - 3 $
$ 5x + 2y = -6 $

Step 2: Convert the second equation to slope-intercept form

To compare the equations, convert the second equation to the slope-intercept form $ y = mx + b $.

Starting with: \[ 5x + 2y = -6 \]

Solve for $ y $: \[ 2y = -5x - 6 \] \[ y = -\frac{5}{2}x - 3 \]

Step 3: Compare the equations

Now, both equations are in the form $ y = -\frac{5}{2}x - 3 $.

Final Answer

Since both equations are identical, the system is consistent dependent. This means the system has infinitely many solutions.

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