7. Systems of Equations & Matrices

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.

$10x-4y=5$

$5x-4y=1$

Use the substitution or elimination method to solve each system of equations. Identify any inconsistent systems or systems with infinitely many solutions. If a system has infinitely many solutions, write the solution set with y arbitrary.

2x + 6y = 6

5x + 9y = 9

Determine whether the given ordered pair is a solution of the system. $(2,3)$

$\begin{cases}x + 3y = 11 \\x - 5y = -13\end{cases}$

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.

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