# Tutor profile: Jessica L.

## Questions

### Subject: Spanish

Escribe un párrafo sobre la historia de salsa.

Salsa is esentialmente cubano y con mucho estilo. Originó por puerto rico y otras partes latinas. Había otras mezclas latinas como el pop, jazz, rock, y R&B. salsa es la música más jugada en los antros. También es la música más essential latina del mundo. Peter Manuel había llamado a la salsa la más popular para bailar entre los puertorriqueños y cubanos. Pero una de la más dinámicas y significantes musicales fueron durante los 70’s y 80’s.

### Subject: Writing

How can the passage below be rewritten to better accomodate flow, tone, vocabulary, grammar, etc? It was a fine summer day with colorful leaves and wind and warm sun and children with ice cream in the park. Alex had her book. Alex flipped through the pages reading kind of fast. Soon the sounds of the wind getting louder and day getting darker made Alex get up and leave.

It was a fine summer day dotted with a myriad of red and yellow leaves. The sun shone down upon the children gleefully holding their ice cream cones while the wind flew among them. Sitting upon a bench, Alex flipped the pages of her book - perusing it without haste. Soon the howling of the wind drew her attention as did the gradual disappearance of the sun; Alex tucked her book under her arm and headed home.

### Subject: Algebra

Solve the following for x, y, and z: x + 2y + 5z = -10 10x + 2y + 3z = 5 7x + 3y + 2z = 7

Labeling the above equations: (1) x + 2y + 5z = -10 (2) 10x + 2y + 3z = 5 (3) 7x + 3y + 2z = 7 We want to find two equations with the same variables, which means we must cancel one variable out by manipulating all three equations with each other. Since equations (1) and (2) already have the same coefficient for y, we can subtract equation (2) from (1) to create equation (4). (2) - (1): 10x + 2y + 3z = 5 x + 2y + 5z = -10 (4) 9x - 2z + 15 Now we must create another equation (5) with the two variables x and z so that we may cancel either x or z using equation (4). To create equation (5) we multiply equations (1) and (3) by factors that would make their y coefficients equal. *NOTE: we cannot use equations (1) and (2) together anymore as we have already derived equation (4) from that combination. Likewise, we could also use a combination of (2) and (3) if we chose to do so. The selection of (1) and (3) is arbitrary and both will lead to the same answers. [2 x (3)] - [3 x (1)]: 14x + 6y +4z = 14 3x + 6y + 15z = -30 (5) 11x - 11z = 44 We can simplify equation (5) by dividing each coefficient by their common factor, 11, to: (5) x - z = 4 Taking (4) and (5) we can eliminate the variable x by multiplying equation (5) by 9 and subtracting so that both x variables in each equation have the same coefficient and cancel each other out. (4) - [9 x (5)]: 9x - 2z = 15 9x - 9z = 36 7z = -21 z = -3 Since we have discovered that z = -3, we can plug it back into our equations to find the other variables. You can plug the value of z = -3 into either equation (4) or (5) and get the same answer for x, but the smart strategy would be to plug z = -3 into the equation that is less complex and yields the answer more easily, which is (5). (5): x - (-3) = 4 x + 3 = 4 x = 1 Now that we have found that x =1 and z = -3, we can plug these two values into any of the equations (1), (2), or (3) and receive the same answer for y. As always, we choose the most efficient way, which would be through equation (1). (1): (1) + 2y + 5(-3) = -10 2y -14 +-10 2y = 4 y = 2 Therefore, the answers are: x = 1, y = 2, and z = -3.

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