Plz help me out! this is from a study guide for the quiz i have today!

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Step-by-step explanation:

The elimination method is multiplying either one or both equations by different factors in order to cancel out one variable when adding both equations.

In the example given, the two equations are

2x + y = -9

3x - 2y = 10

Because you are solving for y, you cannot cancel out the y values and must figure out the factors of multiplication in which the x values cancel.

The least common multiple of 2 and 3 would be 6, because 6 is the first point at which multiples of 2 and 3 meet. (when 2 numbers are prime, the least common multiples are the product of two numbers; 2 and 3 are prime so LCM of 2 and 3 is 2 * 3 = 6)

In order to cancel out the x values, one x must be -6 while the other is +6.

The student successfully multiplies the first equation by +3 in step 2, because he correctly distributes the +3; 3*2x = 6x, 3*y = 3y, 3*9 = 27

6x + 3y = 27

However, the student does not correctly distribute the -2 in step 3;

Although -2 * 3x = -6x, -2 * -2y is not -4y since two negative values multiplied would cancel out and become positive.

The correct distribution of -2 should be:

-2 * 3x = 6x, -2 * -2y = 4y, -2 * 10 = -20

-6x + 4y = -20

The correct answer is then found by adding both equations:

6x - 6x + 3y + 4y = 27 - 20

7y = 7

y = 7/7 = 1

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