Question 984539
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5x-y=8
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The easiest way to show all solutions is a graph:
All points on the line are solutions,
the extended line represents all solutions.
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{{{ graph( 500, 500, -10, 10, -10, 10, 5x-8) }}}
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Determine three different solutions for this equation.
Choose any x and solve for y, or y and solve for x:
Let x=0:
5x-y=8
5(0)-y=8
y=-8
Solution 1: (0,-8)
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Let y=0:
5x-y=8
5x-0=8
5x=8
x=8/5
Solution 2: (8/5,0)
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Let x or y=2
5x-y=8
5(2)-y=8
10-y=8
-y=-2
y=2
Solution 3: (2,2)
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Write an equation that can be paired with the given equation in order to form a system of equations that is inconsistent.
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Parallel lines form inconsistent systems (no common solution:
5x-y=8 Convert to slope intercept form
y=5x-8 Any line with slope=5 will work.
y=5x+8 This line is parallel to the given.
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Inconsistent system:
5x-y=8
5x-y=-8