Solving Systems
Two lines intersect at one point. How many solutions are there?
One
Convert this system into a matrix:
3x + 4y = 6
1x - 2y = 3
[ 3 4 6 ]
[1 -2 3 ]
Two numbers add up to 12 and multiply to 27. What are they?
3 and 9
Solve by graphing:
4x + 12 = 6x + 2
x = 5
In which year did the United States declare independence from Great Britain?
1776
Two lines never intersect. How many solutions are there?
Zero.
The reduced row echelon form of a matrix is given below. How many solutions does the system have?
[1 1 2]
[0 0 0]
Infinitely many.
The South Side Cheer Team is selling concessions at a football game to raise money for new pom-poms. They sell chili dogs and pretzels. Each chili dog was sold for $3 and each pretzel for $1.50. They know they sold 65 items in total, and made $117, but somebody lost the receipts. How many chili dogs and how many pretzels did they sell? Set up, but do not solve, the system.
x + y = 65
3x + 1.5y = 117
What does the solution of an equation represent?
The value which makes the statement or equation true.
What is the third-most spoken language in the United States?
Chinese
Solve:
10x - 2y = 12
2x + 0.5y = 6
(2 , 4)
The reduced row echelon form of a matrix is given below. How many solutions does the system have?
[1 1 2]
[0 0 1]
Zero.
Flying to Chicago with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air. Set up, but do not solve, the system.
x + y = 158
x - y = 112
Solve by graphing:
4x + 12 < 6x + 2
x > 5
Who was King of Great Britain at the time the United States declared independence?
King George III, of the House of Hanover
Solve:
1x + 2y = 3
2x + 4y = 6
Infinitely many solutions.
The reduced row echelon form of a matrix is given below. How many solutions does the system have?
[1 0 2]
[0 1 1]
One. (2, 1)
At a university, 1400 students are enrolled in engineering. There are three times as many in electrical engineering as in mechanical engineering, and half as many in chemical engineering as there are in mechanical engineering. Which system of equations represents the number of students in each program?
3m = e
2c = m
Solve by graphing:
|4x + 12| = |6x + 2|
x = 5 or x = -1.4
Who wrote the Declaration of Independence?
Thomas Jefferson
Solve:
1x + 4y = 1
1x - y = 1
(1, 0)
A system has the solution (3, 4). Using this, determine the values of a, b, c, and d in the reduced row echelon form of the system's matrix:
[a 0 b]
[0 c d]
a, c = 1, b = 3, d = 4
The sum of the measures of the angles of a triangle is 180 degrees. The sum of the measures of the second and third angles is four times the measure of the first angle. The third angle is 12 degrees less than the second. Find the measures of the three angles. Let x = the measure of the first angle, y = the measure of the second angle, and z = the measure of the third angle.
Hint: try setting up a matrix?
x = 36
y = 78
z = 66
Solve by graphing:
|4x + 12| < |6x + 2|
x < -1.4 or x > 5
Who is the current Pope?
Leo XIV