A soccer player kicks a ball. The ball rolls in a straight line, slows down, and stops. What can you conclude about the soccer b
1 answer:
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We have to name a line that "contains" point P. This means that we have to find a line that passes through point P. We can see that line PS/n goes through point P.
We have to find the plane's name. The name (usually a letter) is usually on a corner of the plane, in caps. We could see that there is an F on the bottom left hand corner of the plane, so F is our plane name.
To name an intersection of lines n and m, we have to find the point where they intersect and name it. We could see that point R goes through both lines, so that is our answer.
We have to name a point that does not contain lines l, m, or n. Point W is a point that is not on any of the lines.
Another name for line n is also line PS (add a line on the top of PS when writing this!) because point P and point S are two points on line n.
Line l does not intersect lines n or m because those lines do not go through line l at all.
<h3>Answer: (x,y) = (-2, 5)</h3>
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Explanation:
4x-3y = -23 is the same as 12x-9y = -69 when we multiply both sides by 3
-3x-2y = -4 is the same as -12x-8y = -16 when we multiply both sides by 4
Our updated system looks like this
Notice how we have 12x and -12x. They combine to 0x allowing the x terms to go away.
The y terms combine to -9y+(-8y) = -17y and the right hand sides combine to -69+(-16) = -85
After doing those three sets of additions, we get the new equation -17y = -101 which solves to y = -85/(-17) = 5
The last step is to use this y value to find x
4x-3y = -23
4x-3(5) = -23
4x-15 = -23
4x = -23+15
4x = -8
x = -8/4
x = -2
So the solution is (x,y) = (-2, 5)
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Check:
Let's plug the solution into the first equation
4x-3y = -23
4(-2)-3(5) = -23
-8-15 = -23
-23 = -23
We get a true result. Let's do the same for the second equation
-3x-2y = -4
-3(-2) - 2(5) = -4
6 - 10 = -4
-4 = -4
This result is true as well. So we've confirmed both equations to fully confirm the solution of this system.