Definitions
An inconsistent system of equations can be characterized by this type of solution.
What is no solution?
The quadrant in which the solution to the following system lies:
y = x + 4
y = 2x + 5
What is Quadrant II?
The solution to the system:
x = 4y
2x + 3y = 22
What is (8, 2)?
r + s = -6
r - s = -10
Giannis and LeBron decided to measure a basketball court and found that the width of the court was 44 feet less than the length. If the perimeter was 288 feet, what were the length and width of the court?
What is 94 feet and 50 feet?
The ordered pair that makes both equations true.
What is a solution?
y = 3x - 2
y = -x - 2
The solution to the system
y = x - 2
3x - y = 16
What is (7, 5)?
The solution to the system:
8a + 5b = 9
2a - 5b = -4
What is (1/2, 1)?
Two days at Universal Studios and three days at Knott's Berry Farm costs $510, while 4 days at Universal Studios and 2 days at Knott's Berry Farm costs $580. What was the cost per day at each park?
What is $90 for Universal Studios and $110 for Knott's Berry Farm?
Different forms of the same equations are often referred to as this.
What are dependent equations?
The solution to the system of equations
y = (1/3)x - 3
2x - y = 8
What is (3, -2)?
The solution to the system
3s - 2t = 4
t - 2s = - 1
What is (-2, -5)?
The solution to the system
2a - 4b = 12
-8a + 16b = -48
What is infinitely many solutions?
In a triangle with angles x, y, and z, the measure of angle y is 10 degrees more than three times angle x. The measure of angle z is equal to the sum of angle x and angle y. Find the measures of all three angles.
What is 20 degrees, 70 degrees, and 90 degrees?
In the case of graphing, these types of equations have different (unique) graphs.
What are independent equations?
y - 3x = 3
y = 3x - 2
t + u = 12
t = (1/3)u
The solution to the system:
x + y - z =0
2y - z =1
2x+3y -4z =-4
What is (1,2,3)?
An airplane flies 560 miles in 1.75 hours traveling WITH THE WIND. The return trip later AGAINST THE WIND takes the airplane 2 hours. What is the rate of the airplane and the rate of the wind?
What is 300 mph for the airplane and 20 mph for the wind?