woowheedr

## Answered question

2022-07-06

1.) Given the following equations:
$3x-y=30\phantom{\rule{0ex}{0ex}}5x-3y=10$
What are the values of $x$ and $y$?

### Answer & Explanation

trantegisis

Beginner2022-07-07Added 20 answers

You have what we call a system of two linear equations in two unknowns.
$\begin{array}{}\text{(1)}& 3x-y& =30\text{(2)}& 5x-3y& =10\end{array}$
There are a number of ways you can solve for the $x$,$y$ values that satisfy both equations. One way you can approach this is by substitution: expressing $y$ in equation (1) as a function of $x$, and "plugging" that function into into "$y$" in equation 2:
$\begin{array}{}\text{(1)}& 3x-y=30\phantom{\rule{thickmathspace}{0ex}}⟺\phantom{\rule{thickmathspace}{0ex}}\mathbf{y}\mathbf{=}\mathbf{3}\mathbf{x}\mathbf{-}\mathbf{30}\end{array}$
$\begin{array}{rl}\text{(2)}& 5x-3\mathbf{y}& =105x-3\left(\mathbf{3}\mathbf{x}\mathbf{-}\mathbf{30}\right)& =10\\ 5x-9x+90& =10\\ -4x& =-80\\ \mathbf{x}& =\mathbf{20}\end{array}$
Now, go back to $\left(1\right)$ and "plug in" $x=20$ to solve for $y$:
$\begin{array}{rl}\left(1\right)\phantom{\rule{1em}{0ex}}x=20,\phantom{\rule{1em}{0ex}}3x-y=30& \phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}3\left(20\right)-y=30\\ & \phantom{\rule{thickmathspace}{0ex}}⟺\phantom{\rule{thickmathspace}{0ex}}-y=-30\\ & \phantom{\rule{thickmathspace}{0ex}}⟺\phantom{\rule{thickmathspace}{0ex}}\mathbf{y}\mathbf{=}\mathbf{30}\end{array}$
We have a unique solution to the system given by equations $\left(1\right)$ and $\left(2\right)$, namely, $x=20,\phantom{\rule{thickmathspace}{0ex}}y=30$, and this corresponds to option $\left(a\right)$.

vortoca

Beginner2022-07-08Added 2 answers

Hint:
Just substitute in your equations $x$ and $y$ by the given values and check the answer.

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