2x − 4y = 36 −x + 2y = −18 ( x,y) =

1 answer:

3 0

In this system of equations, x and y have an infinite number of solutions.

We can see this when we try to solve, either by elimination or by substitution.
For substitution, we can take the equation -x + 2y = -18 and rearrange to get x = 2y + 18.
Then we can substitute this into the first equation:

2(2y + 18) - 4y = 36
4y + 36 - 4y = 36
36 = 36
which gives us no solutions.

For elimination, we can multiple the second equation by -2 so that the y coefficient is also -4:
-2(-x + 2y) = -2(-18)
2x - 4y = 36
which just gives us the first equation.

Therefore, we can deduce that any solution that would work for one equation will work for the other equation, so there are an infinite number of solutions.

I hope this helps! Let me know if you have any questions :)

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The 7th grade class experienced a 15% decrease in enrollment. Last year, the 7th grade class had 280 students. How many students

Monica [59]

238 students are enrolled in the 7th grade class this year

Solution:

Given that

Percentage decrease in number of students enrolled in 7th grade = 15%

Number of students enrolled last year = 280

Need to determine number of students enrolled in 7th grade this year.

Lets assume number of students enrolled this year = x

Percentage decrease in enrollment = (Number of student enrolled last year – Number of students enrolled this year) whole divided by number of students enrolled last year multiplied by 100

$\begin{array}{l}{\Rightarrow 15=\frac{280-x}{280} \times 100} \\\\ {=>15 \times 280=28000-100 x} \\\\ {=>100 \mathrm{x}=28000-4200=23800} \\\\ {\Rightarrow x=\frac{23800}{100}} \\\\ {\Rightarrow x=238}\end{array}$