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sineoko [7]
3 years ago
15

What is the solution to the system of equations y = -4x - 19 and y = 2x - 1 in (a, b) form

Mathematics
1 answer:
Temka [501]3 years ago
5 0

For this system of equation I used substitution:

Step 1: Every time you see a y in the equation y = 2x - 1 replace it with -4x - 19

-4x - 19 = 2x - 1

Step 2: Isolate x

(-4x + 4x) - 19 = (2x + 4x) - 1

-19 = 6x - 1

-19 + 1 = 6x + (- 1 + 1)

-18 = 6x

x = -3

Step 3: To solve for y replace x in the equation y = 2x - 1 with -3

y = 2(-3) - 1

y = -6 - 1

y = -7

(-3, -7)

Check:

-7 = -4(-3) - 19

-7 = 12 - 19

-7 = -7 --------------------------------> Correct!

-7 = 2(-3) - 1

-7 = -6 - 1

-7 = -7 --------------------------------> Correct!

Hope this helped!

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4 0
2 years ago
Solve the following system of equations using matrices​ (row operations).
Stells [14]

Answer:

(6,3,0)

Step-by-step explanation:

Given,

x -  y + 0z  =  3

6x -  0y - 2z = 36

0x + 6y + 2z = 18

You have the following augmented matrix:

(1) 1     -1     0      3

(2) 6    0   -2      36

(3) 0    6    2       18

Let's (3) add to (2) and divide by 6

(1)  1    -1    0       3

(2) 1     1    0       9

(3) 0    6   2       18

Now, let's (2) add  to (1) and divide by 2

(1)  1   0    0     6

(2) 1    1    0     9

(3) 0   6   2     18

Let's (3) ÷ 2

(1)  1    0   0     6

(2) 1    1   0      9

(3) 0   3   1      9  

Let's (1) subtract from (2)

(1)  1   0   0     6

(2) 0   1   0     3

(3) 0   3   1     9

Finally, let's (2) multiply by 3 and subtract from (3)

(1)  1   0   0     6

(2) 0   1   0     3

(3) 0   0   1     0

Thus,

x = 6, y = 3 and z = 0

The answer is (6, 3, 0)

We have to verify the answer

6 - 3 = 3  ⇒⇒ 3 = 3

6*6 - 5*0 = 36   ⇒⇒ 36 = 36

6*3 + 2*0 = 18    ⇒⇒ 18 = 18  

6 0
3 years ago
24. A tank can be filled by a pipe in 30 minutes and emptied by another pipe in 50 minutes. How many minutes will it take to fil
OleMash [197]

Answer:

75 minutes

Step-by-step explanation:

The rate at which the tank is filled up, F, and emptied, E, are respectively:

F=\frac{V}{30}*60 = 2V/hour\\E=\frac{V}{50}*60 = 1.2V/hour

Since V is the full volume of the tank, the time required to fill the tank if both pipes are open is given by:

F-E=2V/hour-1.2V/hour = 0.8V/hour\\t= \frac{1}{0.8}=1.25\ hours = 75\ minutes

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4 0
3 years ago
Which is the correct simplified version of the expression shown below
FinnZ [79.3K]

Answer:

D. -2x+12

Step-by-step explanation:

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:) hope this helps

8 0
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Which ratio is equivalent to 9:180
Mamont248 [21]

Step-by-step explanation:

B 12:240

hope it helps you

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2 years ago
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