Simultaneous Equations

$\begin{array}{}\text{(1)}& 19s+12t=82\end{array}$

$\begin{array}{}\text{(2)}& 5s+4t=30\end{array}$

The point of the exercise is to find the values of t and s.

-So what I've done is label the first equation 1 and the second equation 2, as normal.

-Then I multiplied equation 2 by 3 to make the value of t the same on both equations and labelled this, new equation, equation 3:

$\begin{array}{}\text{(3)}& 15s+12t=90\end{array}$

-Then I took equation 3 from equation 2 to breaking it down to find the value of s.

(3) - (2)

$4s=8$

$s=2$

-So, at this point I have worked out that s=2.

-The problem, for me, is when I substitute the value of s back into equation 1. the value of t is a recurring number of 6.

-Have i done something wrong?

$\begin{array}{}\text{(1)}& 19s+12t=82\end{array}$

$\begin{array}{}\text{(2)}& 5s+4t=30\end{array}$

The point of the exercise is to find the values of t and s.

-So what I've done is label the first equation 1 and the second equation 2, as normal.

-Then I multiplied equation 2 by 3 to make the value of t the same on both equations and labelled this, new equation, equation 3:

$\begin{array}{}\text{(3)}& 15s+12t=90\end{array}$

-Then I took equation 3 from equation 2 to breaking it down to find the value of s.

(3) - (2)

$4s=8$

$s=2$

-So, at this point I have worked out that s=2.

-The problem, for me, is when I substitute the value of s back into equation 1. the value of t is a recurring number of 6.

-Have i done something wrong?