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RSB [31]
2 years ago
8

Select all the statements that are true for the following systems of equations

Mathematics
1 answer:
Aleks [24]2 years ago
5 0

Answer:

A. System C simplifies to 2x - 3y = 4 and 4x - y = 54 by dividing the second equation by three (3).

B. Systems A and C have the same solutions.

C. Systems A and B have different solutions.

Step-by-step explanation:

Given the following system of equations;

<em><u>System A</u></em>

2x - 3y = 4  .....equation 1

4x - y = 18  .......equation 2

We would solve the above equations using the elimination method;

Multiplying eqn 1 by 2;

2*(2x) - 2*(3y) = 4*2

4x - 6y = 8  ...... equation 3

Subtracting eqn 2 from eqn 3;

(4x - 4x) + (-6y - (-y)) = 8 - 18

0 + (-6y + y) = -10

-5y = -10

5y = 10

y = \frac {10}{5}

y = 2

To find the value of x;

2x - 3y = 4

2x - 3(2) = 4

2x - 6 = 4

2x = 4 + 6

2x = 10

x = \frac {10}{2}

x = 5

<em><u>Solutions (x, y) = (5, 2)</u></em>

<u><em>System B</em></u>

3x - 4y = 5  ..... equation 1

y = 5x + 3  ..... equation 2

We would solve the equations using substitution method;

Substituting eqn 2 into eqn 1, we have;

3x - 4(5x + 3) = 5

3x - 20x - 12 = 5

-17x - 12 = 5

-17x = 12 + 5

-17x = 17

x = \frac {-17}{17}

x = -1

To find the value of y;

y = 5x + 3

y = 5(-1) + 3

y = -5 + 3

y = -2

<u><em>Solutions (x, y) = (-1, -2)</em></u>

<u><em>System C</em></u>

2x - 3y = 4  ..... equation 1

12x - 3y = 54  ...... equation 2

We would solve the above equations using the elimination method;

Subtracting eqn 2 from eqn 1;

(2x - 12x) + (-3y -(-3y)) = 4 - 54

-10x + (-3y + 3y) = -50

-10x + 0 = -50

-10x = -50

10x = 50

x = \frac {50}{10}

x = 5

To find the value of y;

2x - 3y = 4

2(5) - 3y = 4

10 - 3y = 4

3y = 10 - 4

3y = 6

y = \frac {6}{3}

y = 2

<u><em>Solutions (x, y) = (5, 2)</em></u>

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Answer:

between 8.36 and 8.37

Step-by-step explanation:

\sqrt{70} =8.3666

Hope this helps

3 0
2 years ago
How do you do this (-4,6) and (3,-7) to find the distance between each pair of points
poizon [28]
You use x1-x2 over y1-y2
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3 years ago
What are the relative frequencies, to the nearest hundredth, of the rows of the two-way table? Drag and drop the values into the
quester [9]

Answer:

.25             .75

.44            .56

Step-by-step explanation:

To find the relative frequency, we take the part over the total.

Since this  is a relative frequency table, the total for each row is 1

Group 1 A  = 15/ (15+45) = 15/60 = .25

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8 0
3 years ago
Shaneya purchased a membership to play basketball at her local gym. The membership costs $450 for the year, plus she pays $10 to
olga55 [171]

Answer:

55

Step-by-step explanation:

So start with the total 1,000

then take the 1,000 and minus it by the 450 year so then you can see how much money you have left for the times that she can go to the gym to play.

1,000 - 450 = 550

Now you 550 dollars because basic math. Then you divide the number you got which the number you got was 550 so 550÷10 you divide it by 10 because the rent is 10 each time.

550 ÷ 10 = <u>55</u>

Now you get 55 so that means she can got to the gym 55 times before she goes over 1,000 dollars!

Hoped this helped. Don't forget a middle school person did this so I bet you could have too!

6 0
3 years ago
Please help! I have no idea how to do this.
dlinn [17]

11.  y=-1/3x-4

Plug the slope into m in y=mx+b and  then plug in your point and solve for b. You get C

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13.   Perpendicular means that the slope is the opposite reciprocal so you flip it and multiply it by -1. You then plug that in for your slope and plug in your points and you get A, y=9x+13

3 0
3 years ago
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