Algebra II
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4.7 Inverse Matrices and Systems
I. Solve the following system of equations using inverse matrices.
2. L-6x
+ 19y
fx - 3y
= -1= 6
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0
-y + 2z = 4
.
x + y - z = -10
2x + 3z = 1
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II. Write a system of equations then solve using inverse matrices.
1. A change machine contains nickels, dimes, and quarters. There are 75 coins in the machine,
and the value of the coins is $7.25. There are 5 times as many nickels as dimes. Find the number
2. Conner invested $10,000 for one year in three different investments. The investments paid
simple interest of 5%, 6%, and 7%, respectively, and he received a total of $610 in interest for
the year. He invested $3000 more at 5% than 6%. Find the amount invested at each rate.
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3. A manufacturer of educational supplies makes plastic shapes to hang in the classrooms. A
package of shapes contains squares, pentagons, and hexagons. There are 24 shapes in the
package with a total of 112 sides. If there are 10 more squares than pentagons, find the number
of each shape in the package. " "
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4. The sum of the digits on a three digit number is 18. Three times the tens cligit minus 5ÿimes
the units digit is 17. If 4 times the units digit is added to twice the hundreds digit, the result is
22. Find the number.
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5. A manufacturer sells pencils and erasers in packages. The prices of a package of five erasers
and two pencils are $0.23. The prices of a package of seven erasers and five pencils are $0.41.
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Find the price of one eraser and one pencil.
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6. At a firefighter's pancake breakfast, the firefighters served 345 people and raised $1395.
If the cost of an adult ticket to the pancake breakfast was $5 and the cost of a child's ticket
was $3. What was the number of adult and children tickets sold at the breakfast?
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