Exam 4: Systems of Linear Equations

Solve the system by substitution. Substitute the expression in the second equation into the first equation and solve. If the system is dependent or inconsistent , or if there is no solution , indicate this.

Two positive numbers have a difference of The larger number is one more than twice the smaller. Find the two numbers.

Solve the system by eliminating the variable.

The difference of two positive numbers is The larger is twice the smaller decreased by Find the two numbers.

How much 47% antifreeze solution and 37% antifreeze solution should be combined to give 50 gallons of 43% antifreeze solution? __________ gallons of 47% solution __________ gallons of 37% solution

Solve the system of linear equations by the elimination method. If the system is dependent or inconsistent , indicate this.

A mixture of 13% disinfectant solution is to be made from 16% and 12% disinfectant solutions. How much of each solution should be used if 40 gallons of 13% solution are needed? __________ gallons of 16% solution __________ gallons of 12% solution

Solve the system of linear equations by graphing.

Daniel is trying to decide whether to buy a car or a truck. The truck he is considering will cost him a month in loan payments, and it gets miles per gallon in gas mileage. The car will cost a month in loan payments, but it gets miles per gallon in gas mileage. Daniel estimates that he will pay per gallon for gas. This means that the monthly cost to drive the truck miles will be The total monthly cost to drive the car miles will be The following figure shows the graph of each equation. At how many miles do the car and the truck cost the same to operate?

The sum of two numbers is One number is times the other. Find the numbers.

Solve the system by substitution. Substitute the expression in the second equation into the first equation and solve. If the system is dependent or inconsistent , or if there is no solution , indicate this.

Solve the system of linear equations by graphing.

One number is more than times another. Their sum is Find the two numbers.

Solve the system of linear equations by elimination. If the system is dependent or inconsistent , indicate this.

Solve the system of linear equations by graphing.

Jane is deciding between two sales positions. She can work for Marcy s and receive per hour or for Gigi s, where she earns per hour but also receives a $30 commission per week. The two lines in the following figure represent the money Jane will make for working at each of the jobs. . From the sketch of the graphed lines, how many hours would Jane have to work to earn the same amount at each of the positions? . If Jane expects to work less than hours a week, which job should she choose? . If Jane expects to work more than hours a week, which job should she choose?

If a -inch rope is to be cut into two pieces so that one piece is inches longer than twice the other, how long is each piece?

Solve the system of linear equations by graphing.

The Bishop's Peak 4H club is having its annual fundraising dinner. Adults pay $30 apiece and children pay $15 apiece. If the number of adult tickets sold is twice the number of children's tickets sold, and the total income for the dinner is $3,000, how many of each kind of ticket did the 4H club sell? __________ adult tickets __________ children tickets

Solve the system by solving one of the equations for or and then use the substitution method. If the lines coincide, answer dependent . If the lines are parallel, answer no solution .