1) To solve this system of equations by elimination, what operation could be used to eliminate the y-variable and find the value of x?
2x - 4y = 6
-3x + 3y = 12
A) add 3 times the second equation to 4 times the first equation
B) add 4 times the second equation to 3 times the first equation
C) subtract 3 times the second equation from 4 times the first equation
D) subtract 4 times the second equation from 3 times the first equation

PLEASE HELP!!!

Answer:

Option B is correct.

add 4 times the second equation to 3 times the first equation

Step-by-step explanation:

Answer:

B) add 4 times the second equation to 3 times the first equation

Step-by-step explanation:

So you have these two equations:

2x - 4y = 6

-3x + 3y = 12

In order "to solve this system of equations by elimination" we want to make BOTH of the equations have a term (in this case the y term) and have the same coefficient (that's the number right next to the y) If they are the exactly same number, even the same sign in front, then we would subtract the equations. If they have the same coefficient but different signs, then we would add the equations. This will eliminate the y term completely. So in order to make them have the same coefficient. We'll multiply the first equation by 3 and the second equation by 4

3(2x - 4y = 6)

4(-3x + 3y = 12) multiplying all the way across the equation (distributing)

We'll get

6x -12y = 18

-12x + 12y = 48 Then you are actually adding from the top, down and get one equation from adding the two existing ones together.

-6x = 66 And then you are able to solve it by dividing both sides by -6 to get

x = -11

You can then use either equation and x = -11 to find y. Your solution is the x, y pair. You can check it by putting the x and y into both equations and finding it makes a true statement in both.

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Read the passage below.
You will respond by writing an informational response paragraph.
You will find specific writing directions below the passage.


GOLD IN THE SKY
By Alan E. Nourse

Chapter 1. Trouble Times Two

The sun was glowing dull red as it slipped down behind the curving horizon of Mars, but Gregory Hunter was not able to see it.

There was no viewscreen in the ship's cabin; it was too tiny for that. Greg twisted around in the cockpit that had been built just big enough to hold him, and shifted his long legs against the brace-webbing, trying to get them comfortable.

He knew he was afraid ... but nobody else knew that, not even the captain waiting at the control board on the satellite, and in spite of the fear Greg Hunter would not have traded places at this moment with anyone else in the universe.

He had worked too hard and waited too long for this moment.

He heard the count-down monitor clicking in his ears, and his hands clenched into fists. How far from Mars would he be 10 minutes from now? He didn't know. Farther than any man had ever traveled before in the space of 10 minutes, he knew, and faster. How far and how fast would depend on him alone.

"All set, Greg?" It was the captain's voice in the earphones.

"All set, Captain."

"You understand the program?"

Greg nodded. "24 hours out, 24 hours back, 90 degrees to the ecliptic1, and all the acceleration2 I can stand both ways."

Greg grinned to himself. He thought of the months of conditioning he had gone through to prepare for this run ... the hours in the centrifuge to build up his tolerance to acceleration, the careful diet, the rigorous hours of physical conditioning. It was only one experiment, one tiny step in the work that could someday give men the stars, but to Gregory Hunter at this moment it was everything.

"Good luck, then." The captain cut off, and the blastoff buzzer sounded.

He was off. His heart hammered in his throat, and his eyes ached fiercely, but he paid no attention. His finger crept to the air-speed indicator, then to the cut-off switch. When the pressure became too great, when he began to black out, he would press it.

But not yet. It was speed they wanted; they had to know how much acceleration a man could take for how long and still survive, and now it was up to him to show them.

Fleetingly, he thought of Tom ... poor old stick-in-the-mud Tom, working away in his grubby little Mars-bound laboratory, watching bacteria grow. Tom could never have qualified for a job like this. Tom couldn't even go into free-fall for 10 minutes without getting sick all over the place. Greg felt a surge of pity for his brother, and then a twinge of malicious anticipation. Wait until Tom heard the reports on this run! It was all right to spend your time poking around with bottles and test tubes if you couldn't do anything else, but it took something special to pilot an XP ship for Project Star-Jump. And after this run was over, even Tom would have to admit it....

There was a lurch, and quite suddenly the enormous pressure was gone.

Something was wrong. He hadn't pushed the cut-off button, yet the ship's engines were suddenly silent. He jabbed at the power switch. Nothing happened. Then the side-jets sputted, and he was slammed sideways into the cot.

He snapped on the radio speaker. "Control ... can you hear me? Something's gone wrong out here...."

1The great circle that is the apparent path of the Sun.

2The process of moving faster or happening more quickly.

------------------------

Now that you have read the passage, you will write an informational response paragraph to answer the following question:

How does this story create a feeling of tension or conflict?

Read the directions carefully so you know what to include in your essay.

Begin your paragraph by rephrasing the question into a topic sentence. Be sure to include the title and the author.
Include 3 or more specific examples, details, or quotes from the passage to support your answers to the prompt.
End with a conclusion sentence to wrap up your ideas.
Proofread your work before submitting.
(100 points)

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