Without using a graph, determine the number of solutions in the following systems of equations, then classify the system.

Use the graph to identify the solution to the system of equations or identify that the system has $0$ or infinitely many solutions. If there is a solution, check that the point satisfies both equations.

Determine the number of solutions the system of equations has without graphing.

Determine the number of solutions the system of equations has without graphing.

Use substitution to solve the following system of linear equations.

$4x+y=1$

$x-y=4$

Use substitution to solve the following system of linear equations.

$4x+2y=7$

$x+5y=4$

Use the elimination method to solve the following system of linear equations.

$2x+y=1$

$3x-y=4$

Use the elimination method to solve the following system of linear equations.

$10x-4y=5$

$5x-4y=1$