Consider this system of two equations:

7x + 9y = 100 (cutting)
13x + 6y = 250 (sewing)

To solve this system by elimination, which of the following are the correct first steps?

(select all correct answers)

Question

Consider this system of two equations:

7x +  9y = 100    (cutting)
13x +  6y = 250    (sewing)

To solve this system by elimination, which of the following are the correct first steps?

(select all correct answers)

BlackTom AI · Accepted Answer

The problem asks for the correct first steps to solve the system by elimination and indicates you may select multiple options.

Option: Multiply cutting by 2/3.
- This choice scales the first equation 7x + 9y = 100 by 2/3 to get (14/3)x + 6y = 200/3. The y-coefficient becomes 6, which matches the y-coefficient in the second equation (6y = 250) thus enabling elimination of y if you subtract the equations. This is a valid first step for elimination as it creates a common coefficient for y between the two equations.

Option: Multiply sewing by 7/13.
- This choice scales the second equation 13x + 6y = 250 by 7/13 to get 7x + (42/13)y = 1750/13. The x-coefficient becomes 7, which matches the x-coefficient in the first equation (7x). This sets up an elimination of x when you subtract the equations. This is another valid first step for elimination because it aligns the x terms.

Option: Multiply cutting by 2.5.
- Here 2.5 is 5/2. If you multiply the first equation by 5/2, you get (35/2)x + (45/2)y = 250. While this is a valid scaled form, it does not by itself directly produce a common coefficient with the second equation for either x or y without additional steps. It’s not a straightforward elimination setup in one subtraction with the given second equation, so it’s not one of the standard clean first steps for elimination.

Option: Multiply cutting by 7/13.
- This scales the first equation to (49/13)x + (63/13)y = 700/13. The resulting coefficients do not match the second equation’s coefficients in a way that immediately enables a single elimination after one subtraction, unlike the cases in the correct options. Therefore, this is not considered a correct first elimination step.

Option: Multiply sewing by 7 and sewing by 13.
- This option suggests applying two multipliers to the same equation (or both equations) in a way that’s not consistent with a single, standard elimination step. Proper elimination requires a single consistent scaling of each equation to create a common coefficient for one variable. Using both multipliers in the manner described would be unconventional and does not reflect a valid first-step operation as typically taught. Hence, this is not a correct first-step choice in this context.

Consider this system of two equations: 7x + 9y = 100 (cutting) 13x + 6y = 250 (sewing) To solve this system by elimination, which of the following are the correct first steps? (select all correct answers)多项选择题

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