Question

QUESTION 1

What is the solution set for x + 6 > 2?



{x:x > -8}


{x:x > -4}


{x:x > 4}


{x:x > 8}



QUESTION 13

How many solutions does the system 9x+y=3 over 9x-y=7 have?



infinitely many


none


one


none of the above

QUESTION 17

Solve the system 2x+3y=5 over 3x+2y=0 by substitution.



(2, 3)


(3, 2)


(3, -2)


(-2, 3)

Answer 1

QUESTION 1

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Step 1 ) Subtract 6 from both sides.

x + 6 > 2

x + 6 - 6 > 2 - 6

x > -4

So, the best solution to the equation x + 6 > 2 would be...

B ) x > -4

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QUESTION 13

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Solved using matrix.

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Step 1 ) Rewrite as matrix.

`\left[\begin{array}{ccc}9&1&3\\9&-1&7\end{array}\right]`

Step 2 ) Do Row2 - Row1 and put the value as the new row2.

`\left[\begin{array}{ccc}9&1&3\\9&-1&7\end{array}\right]`

`\left[\begin{array}{ccc}9&1&3\\0&-2&4\end{array}\right]`

Step 3 ) Simplify.

`\left[\begin{array}{ccc}9&1&3\\0&-2&4\end{array}\right]`

`\left[\begin{array}{ccc}9&1&3\\0&1&-2\end{array}\right]`

Step 4 ) Do Row1 - Row2 and put the value as the new Row1.

`\left[\begin{array}{ccc}9&1&3\\0&1&-2\end{array}\right]`

`\left[\begin{array}{ccc}9&0&5\\0&1&-2\end{array}\right]`

Step 5 ) Simplify.

`\left[\begin{array}{ccc}9&0&5\\0&1&-2\end{array}\right]`

`\left[\begin{array}{ccc}1&0&(5)/(9)\\0&1&-2\end{array}\right]`

So, since the solution is x equals 5 over 9 and y equals -2, the amount of solutions is...

C ) One

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QUESTION 17

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Step 1 ) Solve for x in 2x - 3y = 5.

2x - 3y = 5

2x - 3y + 3y = 5 + 3y

2x = 5 + 3y

`\displaystyle(2x)/(2) = (5 + 3y)/(2)`

`\displaystyle\ x = (5+3y)/(2)`

Step 2 ) Place the value of x into 3x - 2y = 0.

3x - 2y = 0

3 ×
`\displaystyle(5+3y)/(2) -2y=0`

`\displaystyle(3(5+3y))/(2) -2y=0`

Step 3 ) Solve for y in the new equation.

`\displaystyle(3(5+3y))/(2) -2y=0`

3 ( 5 + 3y ) - 4y = 0

15 + 9y - 4y = 0

15 + 5y = 0

5y = -15

`\displaystyle(5y)/(5) = (-15)/(5)`

`\displaystyle\ y = -(15)/(5)`

y = -3

Step 3 ) Place the value of y into the value of x.

`\displaystyle\ x = (5 + 3y)/(2)`

`\displaystyle\ x = (5 + 3 * -3)/(2)`

x = -2

So, in 2x - 3y = 5 ; 3x - 2y = 0...

x = -2; y = -3

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- Marlon Nunez