How can we get system B for system A?

And

Are the systems equivalent?​

Answer: Subtract the equations in system A.

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Explanation:

The first equation of each system is the same, so we'll try to transform the second equation of system A into the second equation of system B.

There are probably a number of ways to do this, but the quickest way that I can see is to subtract the equations of each system.

For system A, notice how the x terms line up and subtract to 5x-4x = 1x = x. In that same system, we have the y terms subtract to y minus (-7y) = y-(-7y) = y+7y = 8y

So far we have x and 8y as the results. So the left side is x+8y, which matches with the x+8y in the second equation of system B. So far so good.

Now we subtract the values on the right hand sides of each equation of system A. We get 3-8 which turns into -5, which also matches with the -5 in the second equation of system B.

Overall, subtracting the two equations of system A leads to x+8y = -5, which is the second equation of system B.

18% of the the students at a school are in year 8 and 16% of the students are in year 9. If the school has 126 tera 8 students, determine the number of year 9 students.​

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