Systems
Two or more equations with the same set of variables.
What is a system of equations?
A solution to a system is made up of these two values.
What variable would you substitute for in this system?
y = 4x + 2
y = 3x + 1
y
Define x and y from the following problem:
Alex and Eva are saving money. Alex starts with $500 in his savings account and adds $10 per week. Eva starts with $50 in her savings account and adds $20 each week.
x - Time (weeks)
y - Total money saved ($)
This type of equation has two operations to get rid of in order to solve it.
What is a two-step equation?
The solution to a system of equations.
What is an intersection point?
When graphing a system, this solution occurs when your linear graphs are parallel to each other.
What is no solution?
What variable would you substitute for in this system?
x = 3y + 1
2x + 4y = 12
x
Create a system of equations for the following problem:
Alex and Eva are saving money. Alex starts with $500 in his savings account and adds $10 per week. Eva starts with $50 in her savings account and adds $20 each week.
Alex: y = 10x + 500
Eva: y = 20x + 50
The three types of solutions a system of equations can have.
What is one solution, no solution, and infinite solutions?
Solve this system by graphing. Show your teacher your work.
y = 3x - 1
y = 1/2x + 4
(2,5)
Solve this system using substitution. Show your teacher your work.
y = 2x + 4
y = 4x + 8
(-2,0)
If the solution to the problem with Alex and Eva is (4,650), what does that mean in the context of the problem?
It means Alex and Eva will BOTH have $650 in 4 weeks of saving their money.
What type of solution does this system have?
y = -2x + 4
y = 4x + 1
One solution
Without solving, how many solutions does this system have?
y = 2x + 3
y = 2x - 5
No solution.
When graphing a system, this solution occurs when your linear graphs are completely overlapping.
What is infinite solutions?
Solve this system using substitution. Show your teacher your work.
2x + 6y = 22
x = 2y - 4
(3,2)
Solve the system:
Alex and Eva are saving money. Alex starts with $500 in his savings account and adds $10 per week. Eva starts with $50 in her savings account and adds $20 each week.
(45,950)
Vertical/Horizontal is a strategy used to find the slope in a linear relationship. What geometric shape is this used for?
Without solving, how many solutions does this system have?
2x + 3y = 10
3y + 2x = 10
Infinite solutions.
Solve this system by graphing. Show your teacher your work.
3x + y = 1
y + 3x = 4
No solution
Solve this system using substitution. Show your teacher your work.
x + 2y = 10
3x + 4y = 20
(0,5)
Who will have more money in their account after 30 weeks? Show your work to explain your answer.
Alex and Eva are saving money. Alex starts with $500 in his savings account and adds $10 per week. Eva starts with $50 in her savings account and adds $20 each week.
Alex will have $800, Eva will only have $650.
This is used when describing how large or how small to dilate a figure on the coordinate plane.
What is a scale factor?