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Set up a linear system and solve. The sum of two integers is 45. The larger integer is 3 less than twice the smaller. Find the two integers. The sum of two integers is 126. The larger is 18 less than 5 times the smaller. Find the two integers. The sum of two integers is 41. When 3 times the smaller is subtracted from the larger the result is 17. Find the two integers. The sum of two integers is 46. When the larger is subtracted from twice the smaller the result is 2. Find the two integers. The difference of two integers is 11. When twice the larger is subtracted from 3 times the smaller, the result is 3. Find the integers. The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers. The sum of 3 times a larger integer and 2 times a smaller is 15. When 3 times the smaller integer is subtracted from twice the larger, the result is 23. Find the integers. The sum of twice a larger integer and 3 times a smaller is 10. When the 4 times the smaller integer is added to the larger, the result is 0. Find the integers. The difference of twice a smaller integer and 7 times a larger is 4. When 5 times the larger integer is subtracted from 3 times the smaller, the result is −5. Find the integers. The difference of a smaller integer and twice a larger is 0. When 3 times the larger integer is subtracted from 2 times the smaller, the result is −5. Find the integers. The length of a rectangle is 5 more than twice its width. If the perimeter measures 46 meters, then find the dimensions of the rectangle. The width of a rectangle is 2 centimeters less than one-half its length. If the perimeter measures 62 centimeters, then find the dimensions of the rectangle. A partitioned rectangular pen next to a river is constructed with a total 136 feet of fencing (see illustration). If the outer fencing measures 114 feet, then find the dimensions of the pen. A partitioned rectangular pen is constructed with a total 168 feet of fencing (see illustration). If the perimeter measures 138 feet, then find the dimensions of the pen. Find a and b such that the system ax+by=8bx+ay=7 has solution (2,1). (Hint: Substitute the given x- and y-values and solve the resulting linear system in terms of a and b.) Find a and b such that the system ax−by=11bx+ay=13 has solution (3,−1). A line passes through two points (5,−9) and (−3,7). Use these points and y=mx+b to construct a system of two linear equations in terms of m and b and solve it. A line passes through two points (2,7) and (12,−2). Use these points and y=mx+b to construct a system of two linear equations in terms of m and b and solve it. A $5,200 principal is invested in two accounts, one earning 3% interest and another earning 6% interest. If the total interest for the year is $210, then how much is invested in each account? Harrys $2,200 savings is in two accounts. One account earns 2% annual interest and the other earns 4%. His total interest for the year is $69. How much does he have in each account? Janine has two savings accounts totaling $6,500. One account earns 234% annual interest and the other earns 312%. If her total interest for the year is $211, then how much is in each account? Margaret has her total savings of $24,200 in two different CD accounts. One CD earns 4.6% interest and another earns 3.4% interest. If her total interest for the year is $1,007.60, then how much does she have in each CD account? Last year Mandy earned twice as much interest in her Money Market fund as she did in her regular savings account. The total interest from the two accounts was $246. How much interest did she earn in each account? A small business invested $120,000 in two accounts. The account earning 4% annual interest yielded twice as much interest as the account earning 3% annual interest. How much was invested in each account? Sally earns $1,000 per month plus a commission of 2% of sales. Jane earns $200 per month plus 6% of her sales. At what monthly sales figure will both Sally and Jane earn the same amount of pay? The cost of producing specialty book shelves includes an initial set-up fee of $1,200 plus an additional $20 per unit produced. Each shelf can be sold for $60 per unit. Find the number of units that must be produced and sold where the costs equal the revenue generated. Jim was able to purchase a pizza for $12.35 with quarters and dimes. If he uses 71 coins to buy the pizza, then how many of each did he have? A cash register contains $5 bills and $10 bills with a total value of $350. If there are 46 bills total, then how many of each does the register contain? Two families bought tickets for the home basketball game. One family ordered 2 adult tickets and 4 childrens tickets for a total of $36.00. Another family ordered 3 adult tickets and 2 childrens tickets for a total of $32.00. How much did each ticket cost? Two friends found shirts and shorts on sale at a flea market. One bought 4 shirts and 2 shorts for a total of $28.00. The other bought 3 shirts and 3 shorts for a total of $30.75. How much was each shirt and each pair of shorts? A community theater sold 140 tickets to the evening musical for a total of $1,540. Each adult ticket was sold for $12 and each child ticket was sold for $8. How many adult tickets were sold? The campus bookstore sells graphing calculators for $110 and scientific calculators for $16. On the first day of classes 50 calculators were sold for a total of $1,646. How many of each were sold? A jar consisting of only nickels and quarters contains 70 coins. If the total value is $9.10, how many of each coin are in the jar? Jill has $9.20 worth of dimes and quarters. If there are 68 coins in total, how many of each does she have?

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