Estimate the solution to the system of equations.
2 answers:
Answer:
The solution is: x = -1, and y = 8/3
Step-by-step explanation:
Notice that the system of equations can be easily solved via the "elimination" method, by subtracting term by term one equation from the other. Doing such will remove completely the term in "y" (since the terms in "y" are exactly equal in both equations), and leave only an equation containing "x", for which the value can be solved:
Now we use this x-value in either equation to solve for y:
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The easiest way to tell whether lines are parallel, perpendicular, or neither is when they are written in slope-intercept form or y = mx + b. We will begin by putting both of our equations into this format.
The first equation,
is already in slope intercept form. The slope is 1/2 and the y-intercept is -1.
The second equation requires rearranging.
From this equation, we can see that the slope is -1/2 and the y-intercept is -3.
When lines are parallel, they have the same slope. This is not the case with these lines because one has slope of 1/2 and the other has slope of -1/2. Since these are not the same our lines are not parallel.
When lines are perpendicular, the slope of one is the negative reciprocal of the other. That is, if one had slope 2, the other would have slope -1/2. This also is not the case in this problem.
Thus, we conclude that the lines are neither parallel nor perpendicular.
The first equation,
The second equation requires rearranging.
From this equation, we can see that the slope is -1/2 and the y-intercept is -3.
When lines are parallel, they have the same slope. This is not the case with these lines because one has slope of 1/2 and the other has slope of -1/2. Since these are not the same our lines are not parallel.
When lines are perpendicular, the slope of one is the negative reciprocal of the other. That is, if one had slope 2, the other would have slope -1/2. This also is not the case in this problem.
Thus, we conclude that the lines are neither parallel nor perpendicular.
A Cube, has all equal sides, namely, the length, width and height
are all equal to each other
so.. notice the picture added here
you have really, 6 squares, stacked up to each other at the edges
so...what is the Area of one of those squares?
well, if the sides are equal, let's say the side is "x" long, then
the Area is
well, you have 6 of those squares, thus
solve for "x", to get one side's length
are all equal to each other
so.. notice the picture added here
you have really, 6 squares, stacked up to each other at the edges
so...what is the Area of one of those squares?
well, if the sides are equal, let's say the side is "x" long, then
the Area is
well, you have 6 of those squares, thus
solve for "x", to get one side's length