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Mariulka [41]
3 years ago
7

The sum of negative 45 times a number and twelve is 117. What is the number?

Mathematics
1 answer:
blagie [28]3 years ago
7 0

Answer:

-2.33

Step-by-step explanation:

Let the number be denoted as "x"

-45x + 12 = 117

-45x = 117-12

-45x = 105

x = 105/-45

x= -2.33

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In order to solve the following system of equations by addition, which of the
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Answer:

Multiply the top equation by -3 and the bottom equation by 2

Step-by-step explanation:

Given <u>system of equations</u>:

\begin{cases}4x-2y=7\\3x-3y=15 \end{cases}

To solve the given system of equations by addition, make one of the variables in both equations <u>sum to zero</u>.  To do this, the chosen variable must have the <u>same coefficient</u>, but it should be <u>negative</u> in one equation and <u>positive</u> in the other, so that when the two equations are added together, the variable is <u>eliminated</u>.

<u>To eliminate the </u><u>variable y</u>:

Multiply the top equation by -3 to make the coefficient of the y variable 6:

\implies -3(4x-2y=7) \implies -12x+6y=-21

Multiply the bottom equation by 2 to make the coefficient of the y variable -6:

\implies 2(3x-3y=15) \implies 6x-6y=30

Add the two equations together to <u>eliminate y</u>:

\begin{array}{l r r}& -12x+6y= &-21\\+ & 6x-6y= & 30\\\cline{1-3}& -6x\phantom{))))))} = & 9\end{array}

<u>Solve</u> for x:

\implies -6x=9

\implies x=-\dfrac{9}{6}=-\dfrac{3}{2}

<u>Substitute</u> the found value of x into one of the equations and <u>solve for y</u>:

\implies 3\left(-\dfrac{3}{2}\right)-3y=15

\implies -\dfrac{9}{2}-3y=15

\implies -3y=\dfrac{39}{2}

\implies y=-\dfrac{39}{2 \cdot 3}

\implies y=-\dfrac{13}{2}

Learn more about systems of equations here:

brainly.com/question/27868564

brainly.com/question/27520807

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