1.) Given the following equations: 3 x − y = 30 5 x − 3 y = 10What are the values of x and y?

Question

1.) Given the following equations:  3  x  −  y  =  30    5  x  −  3  y  =  10What are the values of   x and   y?

trantegisis · Accepted Answer

You have what we call a system of two linear equations in two unknowns.

\begin{aligned} (1) & 3 x - y & = 30 \\ (2) & 5 x - 3 y & = 10 \end{aligned}

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{matrix} (1) & 3 x - y = 30 ⟺ y = 3 x - 30 \end{matrix}

\begin{aligned} (2) & 5 x - 3 y & = 10 \\ 5 x - 3 (3 x - 30) & = 10 \\ 5 x - 9 x + 90 & = 10 \\ - 4 x & = - 80 \\ x & = 20 \end{aligned}

Now, go back to

(1)

and "plug in"

x = 20

to solve for

y

:

\begin{aligned} (1) x = 20, 3 x - y = 30 & ⟹ 3 (20) - y = 30 \\ ⟺ - y = - 30 \\ ⟺ y = 30 \end{aligned}

We have a unique solution to the system given by equations

(1)

and

(2)

, namely,

x = 20, y = 30

, and this corresponds to option

(a)

.

vortoca · Accepted Answer

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

1.) Given the following equations: 3 x