Solve by graphing. (If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.) 2x + y = −1
1 6x + 3y = 15
1 answer:
Answer:
The system is INCONSISTENT.
Equation of two parallel lines differ only by a constant.
Step-by-step explanation:
The given equations are:
2x + y = -11
6x + 3y = 15
From the graph we see that these lines are parallel. Any two parallel lines never meet. Hence, they do not have a solution.
Hence, the system is called an Inconsistent system.
Also, note that it can be seen easily from the equations are parallel without the help of a graph.
The equation 6x + 3y = 3(2x + y)
The terms (except for the constant term) are proportional. That means they represent parallel lines.
Hence, the answer.
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The equation in slope intercept form of a line that is a perpendicular bisector of segment AB with endpoints A(-5,5) and B(3,-3) is y = x + 2
<h3><u>Solution:</u></h3>Given, two points are A(-5, 5) and B(3, -3)
We have to find the perpendicular bisector of segment AB.
Now, we know that perpendicular bisector passes through the midpoint of segment.
<em><u>The formula for midpoint is:</u></em>
<em><u>Finding slope of AB:</u></em>
We know that product of slopes of perpendicular lines = -1
So, slope of AB slope of perpendicular bisector = -1
- 1 slope of perpendicular bisector = -1
Slope of perpendicular bisector = 1
We know its slope is 1 and it goes through the midpoint (-1, 1)
<em><u>The slope intercept form is given as:</u></em>
y = mx + c
where "m" is the slope of the line and "c" is the y-intercept
Plug in "m" = 1
y = x + c ---- eqn 1
We can use the coordinates of the midpoint (-1, 1) in this equation to solve for "c" in eqn 1
1 = -1 + c
c = 2
Now substitute c = 2 in eqn 1
y = x + 2
Thus y = x + 2 is the required equation in slope intercept form