Algebra (395 problems)

Solve the system using the graphing method:

If the sum of a number and 9 is decreased by 81, the result is 54. Find the number.

Of the $50,000 that Natasha pocketed on her last real estate deal, $20,000 went to charity. She invested part of the remainder in Dreyfus New Leaders Fund with an annual yield of 16% and the rest in Templeton Growth Fund with an annual yield of 25%. If she made $6060 on these investments in 1 year, then how much did she invest in each fund? Of the $50,000 that Natasha pocketed on her last real estate deal, $20,000 went to charity. She invested part of the remainder in Dreyfus New Leaders Fund with an annual yield of 16% and the rest in Templeton Growth Fund with an annual yield of 25%. If she made $6060 on these investments in 1 year, then how much did she invest in each fund?

Decide if the ordered pair (5, -2) is a solution to the system.

x-2y = 5
2x=4y+10

Find the solutions to the following sets of equations:

Solve the following systems by the substitution method:

The base of an isosceles triangle is 8 in. less than the length of the equal sides. If the perimeter of the triangle is 28 in., find the length of each of the sides.

Solve by substitution. Determine whether the equations are independent, dependent, or inconsistent. 2x – y = 3 and 2y = 4x – 6

Solve the system by substitution.

x + 4y = –4

3x – 3y = –12

y - 2x = -5
4x-2y-6=0

You invested a total of $3,500 in two stocks that paid 6% and 7% annual interest. At the end of the year, the total interest from these investments was $222.75. How much was invested at 7%?

Solve the following systems by the addition method:

Solve the following system by graphing:

Solve the system by the addition (elimination) method: