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3 years ago

Select the coordinate point that is a solution of equations. 2x+y=7; 3x-4y=5

Mathematics

2 answers:

DedPeter [7]3 years ago

7 0

Answer:

D(3,1)

Step-by-step explanation:

The given equations are:

$2x+y=7...(1)$

and

$3x-4y=5...(2)$

Multiply equation (1) by 4.

$\Rightarrow 8x+4y=28...(3)$

Add equation (2) and (3)

$\Rightarrow 11x=33$

Divide through by 11.

$\Rightarrow x=3$

Put x=3 into equation (1)

$2(3)+y=7$

$6+y=7$

$y=7-6$

$y=1$

The solution is (3,1)

The correct choice is D

grandymaker [24]3 years ago

4 0

Answer:

D (3,1)

Step-by-step explanation:

solving simultaneous equations

Arrange equations

2x+y=7

3x-4y=5

make y side cancell by addition by multiplying by 4 and 1 as shown

4{2x+y=7}

1{3x-4y=5}

8x+4y=28

3x-4y=5

11x=33

x=33/11=3

substitute for x=3 in 3x-4y=5

9-4y=5

4=4y

y=1

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Round this whole number Round 10,652 to the nearest ten.

ValentinkaMS [17]

Answer:

10650

Step-by-step explanation:

3 0

3 years ago

I need help on listing the four points that have a distance of 8 from B, thank you!

dolphi86 [110]

Answers:

(12, 3)
(-4, 3)
(4, 11)
(4, -5)

A diagram is shown below.

===========================================================

Explanation:

First we locate point B at (4,3). The '4' in the x position means we've gone 4 units to the right of the origin, and the 3 in the y coordinate means we've gone 3 units up.

Now we need to find four points that are 8 units away from this central location. We'll ignore point A.

What we can do is add 8 to the x coordinate of point B to get x+8 = 4+8 = 12. Keeping the y coordinate the same, the point (12, 3) is exactly 8 units away from (4,3). Think of drawing a number line through those two points. Then we can note there are 8 spaces between (4,3) and (12,3). Or we can say "there are 8 spaces between 4 and 12" since that '3' doesn't really play much of a role in this case.

So (12,3) is one answer.

---------------------------------

Move back to point B(4,3)

Instead of adding 8 to the x coordinate, let's subtract 8 from it

x-8 = 4-8 = -4

Again the y coordinate is kept the same.

The point (-4, 3) is 8 units away from (4,3). The number line distance from -4 to 4 is 8 units.

So (-4,3) is another answer.

----------------------------------

Move back to point B

From this starting point, we can move 8 units up. Doing this means we add 8 to the y coordinate, while the x coordinate is kept intact.

(4,3) turns into (4,11) after doing so.

(4,11) is another answer.

---------------------------------

Move back to point B

From this point, we can move down 8 units to arrive at (4,-5). note how y-8 = 3-8 = -5. The x coordinate is kept the same.

(4,-5) is another answer.

----------------------------------

The four points we found were:

(12, 3)
(-4, 3)
(4, 11)
(4, -5)

which are four possible answers

Those points are found by going 8 units right, 8 units left, 8 units up and 8 units down in that order. Each time we started at point B as our center of operation. The use of the word "center" is done because we can form a circle of radius 8, and the center of the circle is at B(4,3). Any point on the circle's edge is exactly 8 units away from the center point B.

Refer to the diagram below. The four answers are the red points P,Q,R,S. The point T is another point that could be an answer, but it's not as easy to find compared to the four other points.