Use this system of equations to answer the questions that follow. 4x – 9y = 7

–2x + 3y = 4
What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation?

What number would you multiply the second equation by in order to eliminate the y-terms when adding to the first equation?

To eliminate the x-terms, multiply the second equation by 2.

To eliminate the y-terms, multiply the second equation by 3.

Step-by-step explanation:

The first step of solving by elimination requires that you eliminate either the x-terms or y-terms by making the two terms have the same coefficient, but opposite signs.  

So, if you wanted to eliminate the x-terms, you could multiply the second equation so that its x term has the same coefficient as the x-term in the first equation, but with opposite signs. The x-term in the first equation is 4x. The x-term in the second equation is -2x. They already have opposite signs, so we just need the -2x to become -4x. -4x divided by -2x is 2, thus you would multiply the second equation by 2.  

If you wanted to eliminate the y-terms, the process is the same. The y-term in the first equation is -9y and the y-term in the second equation is 3y. Again, they already have opposite signs, we just need 3y to become 9y. 9y divided by 3y is 3, thus you would multiply the second equation by 3.

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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