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. -6x - 4y = 2 -12x + 8y = -8

Solve the problem. -A ceramics workshop makes serving bowls, platters, and bread baskets to sell at its Winter Festival. A serving bowl takes 3 hours to prepare, 2 hours to paint, and 10 hours to fire. A platter takes 17 hours to prepare, 3 hours To paint, and 4 hours to fire. A bread basket takes 4 hours to prepare, 17 hours to paint, and 7 hours to fire. If the Workshop has 94 hours for prep time, 58 hours for painting, and 90 hours for firing, how many of each can be Made?

Solve the system of equations using the addition method. -x - 5y = 3 x - 5y = 3

Write the augmented matrix for the system. -6x + 4y + 7z = 97 -2x + 8y + 6z = 54 6x + 5y + 3z = 72

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. -2x + y = 8 8x + 4y = 32

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. -

Solve the problem. -A chemist needs 140 milliliters of a 54% solution but has only 24% and 94% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Find the solution by graphing the system of equations. -Sybil is having her yard landscaped. She obtained an estimate from two landscaping companies. Company A gave an estimate of $180 for materials and equipment rental plus $60 per hour for labor. Company B gave and Estimate of $220 for materials and equipment rental plus $50 per hour for labor. We can represent this situation with The system of linear equations C = 180 + 60h C = 220 + 50h Where c is the total cost and h is the number of hours of labor. Find the number of hours of labor for the two companies To have the same total cost.

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. -

Solve the problem. -Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 9 times as many dimes as nickels, and the value of the dimes is $9.35 more Than the value of the nickels. How many nickels and dimes does Jamil have?

Solve the system using matrices. -5x - y + 6z = 85 -8x - 8z = -128 4y + z = 15

Solve the problem. -Two angles are complementary if the sum of their measures is 90°. The measure of the first angle is 6° more than two times the second angle. Find the measure of each angle.

Solve the problem. -Marcus earned $5600 during his summer vacation. He invested part of the money at 9% and the rest at 7%. If he received a total of $464 in interest at the end of the year, how much was invested at 9%?

Solve the system using matrices. --5x + 2y - z = -29 x + 6y - 8z = 26 4x + y + z = 42

Solve the system of equations using the addition method. -2x + 40y = 40 4x - 5y = -5

Determine if the following ordered pair satisfies the system of linear equations. -(-2, 6) y = 4x + 14 Y = -3x

Solve the problem. -A twin-engined aircraft can fly 1064 miles from city A to city B in 4 hours with the wind and make the return trip in 7 hours against the wind. What is the speed of the wind?

Determine if the following ordered pair satisfies the system of linear equations. -(-6, -2) 4x + y = -22 3x + 4y = -10

Find the solution to the system of equations by substitution. --4x + y = 14 -5x + 8y = 4

Solve the problem. -A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 3 bags of potato chips for $12.50. Another customer buys 2 hot dogs and 3 bags of potato chips for $8.50. Find the cost of each item.