# Algebra

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1. Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.

5x - 2y = -1

x + 4y = 35

2. Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.

-4x + 9y = 20

-2x - 2y = 10

3. Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for both variables.

The sum of two numbers is 54, and their difference is nine more than the smaller number. Find the numbers.

4. Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for both variables.

Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $135.00 for 3 days and 300 miles, while Mary was charged $250.00 for 5 days and 600 miles. What does Best Rentals charge per day and per mile?

5. Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for the specified variable.

An orchard operator must dilute 11 quarts of a 60%-insecticide solution by adding water. How many quarts of water should be added to get a mixture that is 2% insecticide?

6. Given the pair of linear equations in two variables:

? Find the x- and y-intercepts (if any) for each line. Show your work.

? Plot those intercepts, and graph the two lines on the same chart.

? Apply elimination or substitution to find the coordinates of the point of intersection (if there are no solutions or infinite solutions, state this). Show your work.

x + 8y = 8

9x - 5y = -5

7. Given the pair of linear equations in two variables:

? Find the x- and y-intercepts (if any) for each line. Show your work.

? Plot those intercepts, and graph the two lines on the same chart.

? Apply elimination or substitution to find the coordinates of the point of intersection (if there are no solutions or infinite solutions, state this). Show your work.

-5x + 4y = 8

15x - 12y = 24

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This solution is comprised of detailed step-by-step calculation of the given problems related to Algebra. This solution provides students with a clear perspective of solving linear equations in Algebra.

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