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Ymorist [56]
2 years ago
15

Use the substitution method to solve the system of equations. Choose the correct ordered pair.

Mathematics
1 answer:
Stels [109]2 years ago
3 0

Answer:

x=10

y=-9

Step-by-step explanation:

eqn 2-1

-1x+10=0

x=10

in eqn 1

y=-2 ×10+11

-20+11

-9

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This is Matrix for pre calc
gavmur [86]

The given system of equations in augmented matrix form is

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\-6&1&2&4&-12\\1&-3&-3&5&-20\\-2&5&6&0&12\end{array}\right]

If you need to solve this, first get the matrix in RREF:

  • Add 2(row 1) to row 2, row 1 to -3(row 3), and 2(row 1) to 3(row 4):

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&11&5&-13&37\\0&19&10&4&-10\end{array}\right]

  • Add 11(row 2) to -5(row 3), and 19(row 1) to -5(row 4):

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&-164&132&-1052\end{array}\right]

  • Add 164(row 3) to -91(row 4):

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&0&13080&-39240\end{array}\right]

  • Multiply row 4 by 1/13080:

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&0&1&-3\end{array}\right]

  • Add -153(row 4) to row 3:

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&0&-364\\0&0&0&1&-3\end{array}\right]

  • Multiply row 3 by -1/91:

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]

  • Add 6(row 3) and -8(row 4) to row 2:

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&0&0&-10\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]

  • Multiply row 2 by 1/5:

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&1&0&0&-2\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]

  • Add -2(row 2), 4(row 3), and -2(row 4) to row 1:

\left[\begin{array}{cccc|c}3&0&0&0&3\\0&1&0&0&-2\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]

  • Multiply row 1 by 1/3:

\left[\begin{array}{cccc|c}1&0&0&0&1\\0&1&0&0&-2\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]

So the solution to this system is (w,x,y,z)=(1,-2,4,-3).

6 0
4 years ago
Evaluate:
Anni [7]

Answer:

a) = 4.5

b) = 3.3

Step-by-step explanation:

Before solving our problems given to us let us under stand the rule of cube roots

It says \sqrt[3]{x \times x \times x} = x   -----(A)

Also

\sqrt[3]{x \times x \times x \times y \times y \times y} = x \times y   ---(B)

Now let us see each part one by one

a) we have

\sqrt[3]{64} + \sqrt[3]{0.027} + \sqrt[3]{0.008}

Now 64 = 4 x 4 x 4

0.027 = 0.3 x 0.3 x 0.3

0.008 = 0.2 x 0.2 x 0.2

substituting these values

\sqrt[3]{4 \times 4 \times 4} + \sqrt[3]{0.3 \times 0.3 \times 0.3} + \sqrt[3]{0.2 \times 0.2 \times 0.2}

Applying Rule A in above

=4+0.3+0.2

=4+0.5

4.5

b) we have \sqrt[3]{0.3 \times 0.3 \times 0.3 \times 11 \times 11 \times 11}

Applying the B rule in this

=0.3 \times 11

3.3

4 0
3 years ago
Mika Jena and 5 friends will help run the event. They will wear either a red shirt or a red baseball cap during the event. They
gogolik [260]
4 people will have to wear caps while 3 other will wear shirts.
4x4 = 16
3x8=24
16+24= 40
7 0
3 years ago
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convert 50° Fahrenheit to celsius using the following formula. round your answers to the nearest degree. 5\9 (f°-32) =c°
weqwewe [10]

First you do 50 - 32 an that equals 13, so your answer is 13

8 0
3 years ago
Will give brainliest!!
kirill115 [55]
It’s the one that is marked as (3,3)
8 0
3 years ago
Read 2 more answers
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