An equation written in slope-intercept form is y=mx+b, where m is a constant equal to the slope. Parallel lines have the same slope. So a line parallel to y=-2x+3 is y=-2x+5. Perpendicular lines have slopes which are negative reciprocals of each other. So a line perpendicular to y=-2x+3 is y=1/2x+7. y=2x-1 is neither parallel of perpendicular to y=-2x+3.
Answer: The solution is (3, -2)
This means that x = 3 and y = -2 pair up together.
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Explanation:
The solution is where the two lines cross. Note if we started at the origin (0,0) and moved to the right 3 units, and then down 2 units, we would arrive at the location (3, -2).
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As a way to check, we can plug x = 3 into each equation. We should get y = -2 as a result for each equation
y = (-5/3)x + 3
y = (-5/3)*3 + 3
y = -5+3
y = -2
The first equation is confirmed. Let's check the second equation
y = (1/3)x - 3
y = (1/3)*3 - 3
y = 1 - 3
y = -2
Both equations have the y value equal -2 when x = 3. Therefore, the overall solution is confirmed.
Because there are no parentheses, I'm assuming you're asking for how to factor this using the GCF, which can be done like so:
9−12x+6y
Factor a 3 out of this expression.
3(3 - 4x + 2y)
The expression has been simplified using the distributive property in reverse.
45 = 3x3x5
Or you could simplify it to 3^2x5
3 - 4z - 4 = 3z - 2 - z
-4z - 1 = 2z - 2
2z + 4z = -1 + 2
6z = 1
z = 1/6
Hope this helps!
