Exam 9: Systems of Linear Equations

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 y == 47x x -- 2 3

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

Solve the problem. -Two numbers total 8, and their difference is 16. Find the two numbers.

Solve for the given letter. -

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 - 7y = -9 5x - 7y = 9

Find the solution to the system of equations by substitution. -x + 9y = 9 8x - 5y = -5

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. -4x + 6y = 44 4x + 2y = 52

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 = -50 Y = 9x

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

Find the solution by graphing the system of equations. -The Family Fine Arts Center charges $23 per adult and $12 per senior citizen for its performances. On a recent weekend evening when 446 people paid admission, the total receipts were $6485. We can represent this situation With the system of equations A + s = 446 23a + 12s = 6485 With a representing the adults who attended and s representing the senior citizens who attended. How many who paid Were senior citizens?

Solve the problem. -Jancie has $180,000 to invest to obtain annual income. She wants some of it invested in safe Certificates of Deposit yielding 5%. The rest she wants to invest in AA bonds yielding 12% per year. How much should she Invest in each to realize exactly $18,100 per year?

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

Write the augmented matrix for the system. -9x + 3z = 93 -2y + 8z = 16 5x + 5y + 2z = 93

Solve the system using matrices. -4x + y = 10 -4y + 4z = 4 4x + 5y - 4z = 6

Determine whether the system is inconsistent, dependent, or neither. -4x + y + 2z = 1 -x + 4y + 2z= 5 -9x + 2y - 2z = 3

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. --7y = x + 34 2x + 6y = -36

Determine whether the system is inconsistent, dependent, or neither. -3x + y = 8 -4y - 3z = -29 3x + 5y + 3z = 37

Solve the problem. -Three solutions to the equation Ax + By + Cz = 3 are (1, -4, 2), (1, 8, -4), and (1, 6, -3). Determine the values of A, B, and C and write the equation using the numerical values found.

Find the solution to the system of equations by substitution. -9x + y = 0 -9x + y = -18