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kaheart [24]
3 years ago
12

Estimate the solution of the system x+y=4 2x-y=6 by sketching a graph of each linear function. Then solve the system algebraical

ly. Use your estimate to judge the reasonableness of your solution. The estimated solution is The algebraic solution is The solution is/is not reasonable because​
Mathematics
1 answer:
Juli2301 [7.4K]3 years ago
8 0

Answer:

(10/3, 2/3)

Step-by-step explanation:

You may find it easier to write these two equations x+y=4 2x-y=6 in a column:

x+y=4

2x-y=6

Adding these together will eliminate y:

3x = 10.  Then x = 10/3.

Substituting 10/3 for x in the first equation results in:

10/3 + y = 4

Clear fractions by multiplying all three terms by 3:

10 + 3y = 12

Then 3y = 2, and y = 2/3.

The solution is (10/3, 2/3)

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3 0
3 years ago
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 <em>A</em> and <em>B</em>. " 
__________________________________________________
Explanation:
__________________________________________________
We know that there is a "straight line segment" along the y-axis between
 "point A"  and "point B" ;  since, we are given that: 
___________________________________________
 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.
________________________________________________
  We are asked to find the point that is "half-way" between A and B.
________________________________________________
  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".
___________________________
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.
______________________________________________
So, the "half-way" point would be 1/2  of  6 units, or 3 units.
__________________________________________________
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". 
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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.
______________________________________________
We know the "x-coordinate" is "3" ; so the answer:
_________________________________________________
   " (3,1)  is the point that is halfway between <em>A</em> and<em> B </em>." 
__________________________________________________


8 0
4 years ago
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