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A school sold small and large boxes of fruit for a fundraiser. One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Their sales can be represented in two equations where x represents the price of the small boxes and y represents the price of the large boxes. Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? Check all that apply.

1 The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.

2 The first equation can be multiplied by 5 and the second equation by 12 to eliminate x.

3 The first equation can be multiplied by –7 and the second equation by 13 to eliminate y.

4 The first equation can be multiplied by 7 and the second equation by –13 to eliminate y.

5 The first equation can be multiplied by 12 and the second equation by –5 to eliminate x.

6 The first equation can be multiplied by 7 and the second equation by 13 to eliminate y.

Given that One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Also, x represents the price of the small boxes and y represents the price of the large boxes. Therefore,

The equation for the first student can be written as,

5x + 13y = 232

The equation for the second student can be written as,

12x + 7y = 218

Now, the multiplication that can be done to eliminate the variables are,

1.) The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.

3.) The first equation can be multiplied by –7 and the second equation by 13 to eliminate y.

4.) The first equation can be multiplied by 7 and the second equation by –13 to eliminate y.

5.) The first equation can be multiplied by 12 and the second equation by –5 to eliminate x.

Hence, the correct options are 1, 3, 4, and 5.

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