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KIM [24]
2 years ago
14

Which of the following matrices is the solution matrix for the given system of equations? x + 5y = 11 x - y = 5

Mathematics
1 answer:
givi [52]2 years ago
7 0
<h2>The required solution is x = 6 and y = 11 </h2>

Step-by-step explanation:

Given system of equations are

x+5y = 11 and x-y =5

A= \left[\begin{array}{cc}1&5\\1&-1\end{array}\right]                            X=\left[\begin{array}{c}x\\y\end{array}\right]

and          B= \left[\begin{array}{c}11\\5\end{array}\right]

∴AX=B

adj A = \left[\begin{array}{cc}{-1}&{-5}\\{-1}&1\end{array}\right]

A= \left|\begin{array}{cc}1&5\\1&-1\end{array}\right|=-6

∴A^{-1} =\frac{adj A}{|A|}

So,A^{-1} =\frac{ \left[\begin{array}{cc}{-1}&{-5}\\{-1}&1\end{array}\right]}{-6}

A^{-1} ={ \left[\begin{array}{c \c}  {{\frac{1}{6} }}&{\frac{5}{6}}\ \\  {{\frac{1}{6} }}&{\frac{-1}{6}} \end{array}\right]}

X =A^{-1}\times B

⇒\left[\begin{array}{c}x\\y\end{array}\right] ={ \left[\begin{array}{c \c}  {{\frac{1}{6} }}&{\frac{5}{6}}\ \\  {{\frac{1}{6} }}&{\frac{-1}{6}} \end{array}\right]} \times \left[\begin{array}{c}11\\5\end{array}\right]

⇒\left[\begin{array}{c}x\\y\end{array}\right] ={ \left[\begin{array}{c}  {6}\\  {11} \end{array}\right]}

∴ x= 6 and y = 11

The required solution is x = 6 and y = 11

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Answer:

1. 167.55

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Step-by-step explanation:

For #1 use the formula for volume of cone: V=\pi r^2\frac{h}{3}, and for #2 use the Pythagorean Theorem: a^2+b^2=c^2

7 0
3 years ago
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iris [78.8K]

Step-by-step explanation:

\sqrt{36/4} =\sqrt{36} /\sqrt{4}

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7 0
2 years ago
3x + 2y = 5 5x + 2y = 7 Based on the given system of equations, which of the following is not true? 2x = 2 8x = 12 4y = 4
weqwewe [10]
<h3>Answer:</h3>

8x = 12

<h3>Explanation:</h3>

Subtracting the first equation from the second, you get ...

... (5x +2y) -(3x +2y) = (7) -(5)

... 2x = 2 . . . . . the first answer choice is true

___

Multiplying this expression for x by 4, we get

... 8x = 8 . . . . . the second answer choice (8x=12) is false

___

Adding thee first equation to the second, you get ...

... (3x +2y) +(5x +2y) = (5) +(7)

... 8x +4y = 12

... 8 + 4y = 12 . . . . . . use the value of 8x just computed

... 4y = 4 . . . . . . . . . . subtract 8; the third answer choice is true

_____

<em>Alternate approaches</em>

In short, if you solve the system by any of the methods available, you find x=1 and y=1, so the second answer choice is clearly the correct one:

... 8x ≠ 12

By Cramer's method:

... x = (2·7-2·5)/(2·5-2·3) = 4/4 = 1

... y = (5·5-7·3)/4 = 4/4 = 1

By graphing, see attached.

By substitution (for 2y):

... 5x +(5-3x) =7 . . . . . using 2y=5-3x

... 2x = 2 . . . . . . subtract 5

... x = 1 . . . . . . . .divide by 2

... 5 -3·1 = 2y = 2 . . . . substitute x into the expression for 2y

... y = 1 . . . . . . . divide by 2

By matrix methods, see the second attachment. (x, y) = (1, 1), found in the rightmost column of the result.

6 0
3 years ago
Solve for z:<br><br> 25z+85=90<br><br> z= <br> this confuses me and I need help ;-;
seraphim [82]
Z=1/5

Subtract 85 from both sides which gets you 25z=5.


Divide both sides by 25 which is z=5/25

Simplify which gives us the answer z=1/5.
4 0
2 years ago
Read 2 more answers
I need help plz I don't get this problem
OlgaM077 [116]
To find the answer you need to write equivalent fractions with larger denominators. If you multiply each fraction by 3/3 then your equivalent fractions would be

3/5 × 3/3 = 9/15
4/5 × 3/3 = 12/15

Now we have two fractions that are equivalent to the original fractions and we can easily see that 2 fractions between 9/15 and 12/15 would be...

10/15 and 11/15

(10/15 can reduce to 2/3 so your answers could also be 2/3 and 11/15)
5 0
3 years ago
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