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2 years ago

A system of equations is shown below.

Mathematics

1 answer:

weeeeeb [17]2 years ago

8 0

Answer:

-12

Step-by-step explanation:

Step1: Add 3 to both sides of the equation

2x -3 = 5x +6

+3 +3 = 9

Step2: subtract 5x from both sides of the equation

2x = 5x +9

-5 -5

Step3: divide both sides of the equation by the same term

-3x(/ -3) = 9(/-3)

Step4: multiply -3 with 2

-3x2= -6

Step4: subtract -6 with 3

-6 - 3= -9

Step5: add the -9 to -3

-9 + -3 = -12

ANSWER: -12

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3 years ago

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statuscvo [17]

9514 1404 393

Answer:

(a, b) = (-2, -1)

Step-by-step explanation:

The transpose of the given matrix is ...

$A^T=\left[\begin{array}{ccc}1&2&a\\2&1&2\\2&-2&b\end{array}\right]$

Then the [3,1] term of the product is ...

$(A\cdot A^T)_{31}=\left[\begin{array}{ccc}a&2&b\end{array}\right]\cdot\left[\begin{array}{ccc}1&2&2\end{array}\right]=a+2b+4$

and the [3,2] term is ...

$(A\cdot A^T)_{32}=\left[\begin{array}{ccc}a&2&b\end{array}\right]\cdot\left[\begin{array}{ccc}2&1&-2\end{array}\right]=2a-2b+2$

Both of these terms in the product matrix are 0. We can solve the system of equations by adding these two terms:

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3a +6 = 0

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Substituting for 'a' in term [3,1] gives ...

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2 years ago