Question

0.05x + 0.25y = 33
0.15x + 0.05y = 36

Solve for x and y.

I know to multiply by 100 to get rid of the decimals and then multiply the first equation by -3, but after that, I'm lost.

Answer 1

so the system of equations will give you after the multiplication
$$
0.05x + 0.25y = 33\\
0.15x + 0.05y = 36\\
\implies
\begin{matrix}
5x&+25y&= 3300\\
15x&+5y &= 3600\\
\end{matrix}\\
\text{multiply the bottom one by -5}\\
\begin{matrix}
5x&+25y&= 3300\\
-75x&-25y &= 3600 & \times \color{red}{-5}\\
\hline\\
\end{matrix} \\
$$

Answer 2

so you multiply everything by 100 to get rid of the decimals

5x + 25y = 3300
15x + 5y = 3500

now multiply the first equation by -3

-15x + -75y = -9900
15x +5y = 3500

now we can just add the two equations together, and the x terms will cancel because the first one is negative 15 and the second is positive 15

Answer 3

woops, I missed one number

Answer 4

$$
0.05x + 0.25y = 33\\
0.15x + 0.05y = 36\\
\implies
\begin{matrix}
5x&+25y&= 3300\\
15x&+5y &= 3600\\
\end{matrix}\\
\text{multiply the bottom one by -5}\\
\begin{matrix}
5x&+25y&= 3300\\
-75x&-25y &= -18000 & \times \color{red}{-5}\\
\hline\\
\end{matrix} \\
$$

Answer 5

so, now "add" VERTICALLY accordingly, variable by variable

Answer 6

what do you get for the "x" column, what do you get for the "y" column, what do you get for the "results" column?

Answer 7

So right now I'm at

-75y=-9900
5y= 3600

because I eliminated x first.

-70y = -6300
y = 90?

Answer 8

yes

Answer 9

now that you know what "y" is, plug it in on either equation and solve for "x"

Answer 10

15x + 5(90) = 3600
15x + 450 = 3600
15x = 3150
x = 210?

Answer 11

yes