Question

If 2x - 9y = 14 and 6x = 42 +y, what is the value of the product xy?

Answer 1

The product x time y is zero (0)

Explanation:

Notice that you are given a system of two equations with two unknowns, so, let's proceed to find the unknowns by the method of substitution (easiest since it is very simple to find "y" in terms of 'x" from the second equation).

Then we use that expression to substitute for "y" in the first equation and solve for x:

`6x=42+y\\y=6x-42\\Then:\\2x-9y=14\\can\,\,be\,\,written\,\,as:\\2x-9(6x-42)=14\\2x-54x+372=14\\-52x=-364\\x=(-364)/(-52)\\x=7`

Now we use this result in the substitution equation to find the value of "y":

`y=6x-42\\y=6\,(7)-42\\y=42-42\\y=0`

Then, the product x times y is: 7 times 0 = 0

The product renders zero (0)