Vocabulary
In a system of linear equations, the location where the graphs intersect is referred to as the _____________ to the system.
What is solution.
A system has this many solutions if the two lines intersect at the point (3, -5).
What is one?
y = 3x - 4
x - y = -4
What is (4,8)?
2x - y = 4
7x + 3y = 27
What is (3, 2)
The sum of two numbers is 24. Five times the first number minus the second number is twelve. What are the two numbers?
What are 6 and 18.
Two equations in a system have the same y-intercept but different slopes, how many solutions will this system have?
What is one.
When solving a system of equations by using the elimination method, you end up with the answer 3=3, what is your solution?
What is infinitely many solutions.
-6x - 2y = -8
y = -3x + 4
What are infinite solutions
2x + 7y = 1
x + 5y = 2
What is (-3, 1)
A farmhouse shelters 23 animals. Some are pigs and some are ducks. Altogether there are eighty legs. how many of each animal are there?
What is 6 ducks and 17 pigs.
In a system of equations, this is the best method to use when one of the equations is already solved for one of the variables.
What is the substitution method.
A system will have this many solutions if the equations have the same slope but different y-intercepts.
What is none (or 0)
y = x + 5
y = -3x + 25
What is (5, 10)
2x + 5y = 11
4x + 3y = 1
What is (-2, 3)
A class used eight vehicles to go on a field trip. If they had 43 students attend the trip and a car can hold five students and a van can hold six, how many of each vehicle did they take?
What is 5 cars and 3 vans.
In the elimination method, this is the the goal concerning the coefficients of one of the variables.
What is get them to be opposites.
A system of equations has one solution. What occurs at that solution on the graph of the system?
What is the lines intersect.
y = 2x - 6
y = 4x + 10
What is (-8, -22)
8x + 3y = 4
5y = 7x - 34
What is (2, -4)
Tianna has saved dimes and quarters in her piggy bank. If she has 25 coins and they total $4.00 in value, how many of each coin does she have?
What is 15 dimes, 10 quarters.
These are three methods that can be used to solve a system of linear equations.
What is graphing, substitution and elimination.
What would be the solution to a system of equations, if, when solving it, you end up with 0=8.
What is no solution.
2x + y = 3
4x + 4y = 8
What is (1, 1)
x = y - 1
-x + 1 = -1
What is no solution
Julie subscribes to a sports magazine and a fashion magazine. She received 24 issues this year. The number of fashion issues is six less than twice the number of sports issues. How many of each magazine did she receive?
What is 10 sports and 14 fashion.