Question 243533
First, get both equations into y = mx + b format.
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3x -y = 24
Add y to both sides
3x = 24 + y = y + 24
Subtract 24 from both sides
3x - 24 = y
y = 3x - 24
.
3x + 4y = -6
Subtract 3x from both sides
4y = -6 - 3x = -3x - 6
Divide by 4
{{{y = -(3x)/4 -(6/4) = -(3/4)x - 6/4 = -(3/4)x - 3/2}}}
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Graph:
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{{{
graph(500,500,-10,10,-30,10,3*x-24,-3/4*x-3/2)
}}}
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The lines intersect, so we know the system of equations have a solution, so they're consistent.  That they have only a single solution means they are independent.