Questions:
Systems of Equations
Determine whether the given point is in the solution set to the given system.
1) (-2, -4)
3x + y = -10
4x + 3y = -20
Solve the system by substitution.
2) x + 9y = 53
2x + 9y = 52
Solve the system by addition.
3) x + 2y = 12
4x + 3y = 18
Classify the system as independent, inconsistent, or dependent.
4) x + y = 2
x + y = 5
5) 2x - y = 5
-4x + 2y = -18
Solve the problem.
6) Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $156 for 3 days and 300 miles, while Mary was charged $284 for 5 days and 600 miles. What does Best Rental charge per day and per mile?
Determine whether the given point is in the solution set to the given system.
7) (-3, -1, 4)
2x - 2y - 3z = -16
4x - 3y + 3z = 3
x + y - 5z = -24
Solve the problem.
8) The sum of three numbers is 4. The first, minus the second, plus 4 times the third, is -9. The third, plus 5 times the first, plus the second, is 24. What are the numbers?
Perform the indicated operation and simplify.
9) 3/r + 7/r+1
Solve the system.
10) y = 3x
y = 5x
Solve the system of equations.
11) -3x - y + 8z = 54
-6x + 9y - 4z = 25
5x - 4y + z = -15
Determine whether the given point is in the solution set to the given system.
12) (3, -2)
x - 2y = 7
x2 + y2 = 13
Solve the system.
13) 4x2 - 4y2 = 20
3x2 + 2y2 = 35
Solve the problem.
14) The sum of three numbers is -5. The first, minus the second, plus 4 times the third, is -20. The third, plus 4 times the first, plus the second, is -20. What are the numbers?
15) The sum of the squares of the digits of a positive two-digit number is 20, and the tens digit is 2 more than the units digit. Find the number
16) Find the unknowns on the right side of the partial fraction decomposition.
17) Decompose into partial fractions
Graph the linear inequality.
18) -2x - 4y ≤ 8
Graph the solution set of the system.
19) y ≤ -x2 - 6x - 4
y ≥ x2 + 6x + 4
20. Write a system of inequalities whose solution set is the region shown
