Exam 9: Systems of Linear Equations

Solve the system of equations using the addition method. -x + y = -2 5x + 2y + 2z = -11 X - z = 6

Determine if the following ordered pair satisfies the system of linear equations. -(-4, -3) x + y = 1 X - y = 7

Solve the system using determinants. -5x + 5y - z = 27 x + 6y - 7z = -39 6x + y + z = 40

Solve the problem. -Mr. Alexander earns a weekly salary plus a commission from his position as a salesman. One week his total compensation on sales of $5000 was $1000. The next week his total compensation on sales of $7000 was $1160. Find Mr. Alexander's weekly salary and his commission rate.

Determine whether the system is inconsistent, dependent, or neither. -x + y + z = 8 x - y + 5z = 4 2x + 2y + 2z = 11

Solve the problem. -The sum of the measures of the angles of a triangle is 180°. The smallest angle of the triangle has a measure the measure of the second smallest angle. The largest angle is 18° less than three times the measure of the second smallest angle. Determine the measure of each angle.

Solve the problem. -Three planes are parallel as illustrated below. Is the system consistent, inconsistent, or dependent?

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. -y = x - 6 x - 5y = 30

Solve the system of equations using determinants. -99xx ++ y y == 3158

Solve the system using determinants. -5x - 5z = 10 8x + 9y + 3z = 105 -3x - 2y = -28

Solve the system of equations using determinants. -3x + 5y = 24 2x + y = 2

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. -5x + y = 0 4x - 2y = -14

Solve the problem. -Devon purchased tickets to an air show for 4 adults and 2 children. The total cost was $144. The cost of a child's ticket was $3 less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket.

Solve the system using matrices. -3x + 2y = -3 5x + 8y = 9

Determine if the following ordered pair satisfies the system of linear equations. -(6, 2) 2x = -10 - y 3x = -14 - 2y

Write the augmented matrix for the system. -2x + 8y = 34 9x + 2y = 85

Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations has exactly one solution, no solution, or an infinite number of solutions. -x + y = -4 x + y = 8

Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one solution, no solution, or an infinite number of solutions. -

Solve the system of equations using the addition method. -2x - 2y = 9 10x - 10y = 18

Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state. -