Find the ordered pair $(j,k)$ that satisfies the equations $5j-42k=1$ and $2k-j=3$.
To solve this system of equations, I can use either substitution or elimination. I think substitution might be easier in this case, since I can easily isolate $j$ in terms of $k$ from the second equation. So I will rewrite the second equation as $j=2k-3$. Then I can plug this expression for $j$ into the first equation and get $5(2k-3)-42k=1$. Expanding the parentheses, I get $10k-15-42k=1$. Combining like terms, I get $-32k=16$. Dividing both sides by -32, I get $k=-\frac{1}{2}$. Now that I have $k$, I can plug it back into either equation to find $j$. I will use the second equation again, since it is simpler. So I get $j=2(-\frac{1}{2})-3$. Simplifying, I get $j=-4$. Therefore, the ordered pair $(j,k)$ that satisfies both equations is $(-4,-\frac{1}{2})$. 