What is the solution to the system of equations? y = 1/3x – 10 2x + y = 4

Mathematics

2 answers:

kolezko [41]3 years ago

5 0

The solution is (6, -8) (solved by graphing with Desmos.com/calculator)

serg [7]3 years ago

3 0

Answer:

x=6, y=8

Step-by-step explanation:

First, we can put the sytem of equations in standard form, it holds that

$y-\dfrac{1}{3}x=-10\\\\\\y+2x=4$

then, we can substract the second equation from the first equation to get that

$(\dfrac{-1}{3}-2)x=-10-4\quad\Rightarrow\quad \dfrac{-7}{3}x=-14\\\\\quad\Rightarrow\quad x=6$

Finally, we use this result in the first equation to get that

$y-\dfrac{1}{3}\cdot 6=-10\quad\Rightarrow\quad y-2=-10\quad\Rightarrow y=8$

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The points A(3, 4), B(3, -2), C(-5, -2), and D(-5, 4) form rectangle ABCD. Which point is halfway between A and B?

Dmitriy789 [7]

Answer: " (3,1) is the point that is halfway between A and B. "
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Explanation:
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We know that there is a "straight line segment" along the y-axis between
"point A" and "point B" ; since, we are given that:
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1) Points A, B, C, and D form a rectangle; AND:

2) We are given the coordinates for each of the 4 (FOUR points); AND:

3) The coordinates of "Point A" (3,4) and "Point B" (3, -2) ; have the same "x-coordinate" value.
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We are asked to find the point that is "half-way" between A and B.
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We know that the x-coordinate of this "half-way" point is three.

We can look at the "y-coordinates" of BOTH "Point A" and "Point B".
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which are "4" and "-2", respectively.

Now, let us determine the MAGNITUDE of the number of points along the "y-axis" between "y = 4" and y = -2 .

The answer is: "6" ; since, from y = -2 to 0 , there are 2 points, or 2 "units" from y = -2 to y = 0 ; then, from y = 0 to y = 4, there are 4 points, or 4 "units".

Adding these together, 2 + 4 = 6 units.
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So, the "half-way" point would be 1/2 of 6 units, or 3 units.
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So, from y = -2 to y = 4 ; we could count 3 units between these points, along the "y-axis". Note, we could count "2" units from "y = -2" to "y = 0".
Then we could count one more unit, for a total of 3 units; from y = 0 to y = 1; and that would be the answer (y-coordinate of the point).
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Alternately, or to check this answer, we could determine the "halfway" point along the "y-axis" from "y = 4" to "y = -2" ; by counting 3 units along the "y-axis" ; starting starting with "y = 4" ; note: 4 - 3 = 1 ; which is the "y-coordinate" of our answer; that is: "y = 1" ; and the same y-coordinate we have from the previous (aforementioned) method above.
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We know the "x-coordinate" is "3" ; so the answer:
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" (3,1) is the point that is halfway between A and B ."
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8 0

4 years ago

48 decreased by a number turn phrase into alegrabralc expression

Serhud [2]

Answer:

48-x

Step-by-step explanation:

Decreased means subtraction

Let x be the unknown number

48-x

5 0

3 years ago