Systems of Equations in Two Variables
Determine whether the following system of consistent or inconsistent. If the system is consistent, determine whether the equations are dependent or independent. Do not solve the system.
x + 2y = -3
2x + 4y = 2
What is inconsistent?
Write the system of equations that represents the situation. Do NOT solve.
The sum of the diameters of the largest and smallest pizzas sold at a pizza shop is 35 inches. The difference in their diameters is 7 inches. Find the diameters of the largest and smallest pizzas.
What is
x + y = 35
x - y = 7
Factor x^2 + 4x + 3
What is (x+3)(x+1)
Evaluate sin(pi)
What is 0?
Determine whether the following system of consistent or inconsistent. If the system is consistent, determine whether the equations are dependent or independent. Do not solve the system.
x + 2y = -3
2x - 3y = 7
What is consistent and independent?
Write the system of equations that represents the situation. Do NOT solve.
Janet bought 135 pieces of candy to give away on Halloween. She bought two kinds of candy, paying $0.24 apiece for one kind and $0.18 apiece for the other. If she spent $26.70 for the candy, how many pieces of each kind did she buy?
x + y = 135
0.24x + 0.18y = 26.70
Factor x^2 - 4x - 5
What is (x-5)(x+1)?
Evaluate cos(pi/4)
What is sqrt(2) / 2?
Solve the following system using the graphing method. Write the solution as an ordered pair.
-2x + y = 2
x + y = -1
What is (-1,0)?
Write the system of equations that represents the situation. Do NOT solve.
Last year Mrs. Rodgers invested $40,000. Part was invested at 6% interest rate per year, and the rest was invested in a risky venture at 10% per year. Combined income for the year totaled $3,120. How much did she invest at each rate?
What is
x + y = 40,000
0.06x + 0.10y = 3,120
Factor x^2 - 49
What is (x+7)(x-7)?
Evaluate sin(pi/3)
What is sqrt(3) / 2?
Solve the following system of equations by the substitution method (use exact values in your answer):
y = 2x + 1
5x + 2y = 7
What is (5/9, 19/9)?
Solve the system. Write the answer as an ordered triple.
x - y + z = 6
2y + 3z = 5
2z = 6
What is (1, -2, 3)?
Factor x^2 + x - 6
What is (x+3)(x-2)?
Evaluate tan(5pi/4)
What is 1?
Solve the following system of equations by the substitution method.
4x - y = 8
8x - 2y = 19
Solve the system of equations by the substitution method.
4x + y = -3
-x^2 + y = 1
What is (-2,5)?
Factor 3x^2 - 5x - 2
What is (3x+1)(x-2)
Evaluate sec(pi/6)
What is 2/sqrt(3) or 2sqrt(3) / 3?