Solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.

$\{\begin{array}{c}y=4x+1\\ 3x+2y=13\end{array}$

Solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.

$\{\begin{array}{c}x+4y=14\\ 2x-y=1\end{array}$

A chemist needs to mix a solution that is 34% silver nitrate with one that is 4% silver nitrate to obtain 100 milliliters of a mixture that is 7% silver nitrate. How many milliliters of each of the solutions must be used?

The perimeter of a table tennis top is 28 feet. The difference between 4 times the length and 3 times the width is 21 feet. Find the dimensions.

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Solve each system by the method of your choice.

$\{\begin{array}{c}5y=x^2-1\\ x-y=1\end{array}$