7. Systems of Equations & Matrices

Two Variable Systems of Linear Equations

Open Question
In Exercises 1–4, determine whether the given ordered pair is a solution of the system.(- 3, 5)9x + 7y = 88x - 9y = - 69
Open Question
Solve each system of equations. State whether it is an inconsistent system or has infinitely many solutions. If a system has infinitely many solutions, write the solution set with x arbitrary. See Examples 3 and 4.5x - 5y - 3 = 0 x - y - 12 = 0
Multiple Choice
Use substitution to solve the following system of linear equations.
$4x+y=1$
$x-y=4$
Multiple Choice
Use substitution to solve the following system of linear equations.
$4x+2y=7$
$x+5y=4$
Multiple Choice
Use the elimination method to solve the following system of linear equations.
$2x+y=1$
$3x-y=4$
Multiple Choice
Use the elimination method to solve the following system of linear equations.
$10x-4y=5$
$5x-4y=1$
Multiple Choice
Solve the following system of equations. Classify it as CONSISTENT (INDEPENDENT or DEPENDENT) or INCONSISTENT.
$y=5x-17$
$15x-3y=51$
Multiple Choice
Solve the following system of equations. Classify it as CONSISTENT (INDEPENDENT or DEPENDENT) or INCONSISTENT.
$2x+8y=7$
$x+4y=19$
Open Question
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
Open Question
In Exercises 1–4, determine whether the given ordered pair is a solution of the system.(2, 3)x + 3y = 11x - 5y = - 13
Open Question
In Exercises 1–5, 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.
Open Question
In Exercises 1–5, 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.
Open Question
In Exercises 1–4, determine whether the given ordered pair is a solution of the system.(2, 5)2x + 3y = 17x + 4y = 16
Open Question
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. 1/6x + 1/3y = 81/4x + 1/2y = 12
Open Question
In Exercises 5–18, solve each system by the substitution method.x + y = 4y = 3x