As a Matter of Fact!
This is how many equations are in a system of equations.
2 or more
When plotting the following line on a graph, this is where you would start plotting a point on this axis, and this is how much in which directions you would move to plot the rest of the points:
y = 1/4x + 5
You would plot the first point at 5 on the y-axis.
From there, you would move up 1 and to the right 4 for each point.
This is the solution to the following linear function:
X: 2, 4, 6, 8, 10 , 12, 14, 16
Y1: 1, 3, 5, 7, 9, 11, 13, 15
Y2: 1, 5, 9, 13, 17, 21, 25, 29
(2,1)
These are the 2 equations to make from the following scenario:
Two numbers have the following properties:
1: Their sum is 12
2: X is 4 more than twice Y
X + Y = 12
X = 2Y + 4
This is the solution to the following system of equations:
X = 8
3X + 4Y = 16
X = 8
Y = -2
This is the solution to a system of equations.
The point/coordinate at which the two lines cross.
When plotting the following line on a graph, this is where you would start plotting a point on this axis, and this is how much in which directions you would move to plot the rest of the points:
y = -2x - 4
You would plot the first point at -4 on the y-axis.
From there, you would move down 2 and to the right 1 for each point.
OR
Up 2 to the left 1
This is the solution to the following linear function:
X: 2, 4, 6, 8, 10 , 12, 14, 16
Y1: 1, 3, 5, 7, 9, 11, 13, 15
Y2: 2, 3, 4, 5, 6, 7, 8, 9
(4,3)
Kristin spent $131 on clothes. Pants cost $28 and shirts cost $15. She bought a total of 7 pieces of clothing.
Let x = pants
Let y = shirts
x + y = 7
28x + 15y = 131
This is the solution to the following system of equations:
X + Y = 12
X = 3Y + 4
X = 10
Y = 2
In the following equation, this is the slope, and this is the y-intercept:
y = 2x - 6
Slope = 2
y-intercept = -6
When plotting the following line on a graph, this is where you would start plotting a point on this axis, and this is how much in which directions you would move to plot the rest of the points:
y = -x + 2
You would plot the first point at 2 on the y-axis.
From there, you would move down 1 and to the right 1 for each point.
OR
Up 1 to the left 1
This coordinate is the solution to the following system of equations:
2x + y = 20
y = 2x
CHOICES:
a - (0,20)
b - (10,0)
c - (5, 10)
d - (10,20)
c - (5, 10)
These are the 2 equations to make from the following scenario:
Maya wants to rent a bounce house for one day. She contacted two companies. Company A charges $20 plus $2 per hour. Company B charges $3 per hour.
Y = 2x + 20
Y = 3x
This is the solution to the following system of equations:
3x - y = 12
4x + y = -33
X = -3
Y = -21
This system can be solved best with this method:
y + 4x = 16
y = 2x + 3
substitution
This is what a graph with no solution looks like.
Parallel lines
This is whether or not the following coordinate is a solution to the system of equations, and WHY:
(1,5)
y = 3x + 2
y = -2x + 7
Yes, because when you plug the coordinates in for x and y, the equations are true; 5 = 5.
These are the 2 equations to make from the following scenario:
Mrs. Schutz is buying 2 types of gift cards as prizes to students in her class. She will buy Amazon gift cards that each cost $50. She will also buy Starbucks gift cards that each cost $20. She has $450 to buy a total of 15 gift cards.
x + y = 15
50x +20y = 450
This is the solution to the following system of equations:
2x + 3y = 21
x + y = 3
X = -12
Y = 15
This system can be solved best with this method:
2y + 4x = 16
8y - 4x = 24
Elimination
This is what a graph with infinite solutions looks like.
Same line on top of the same line.
This is whether or not the following coordinate is a solution to the system of equations, and WHY:
(0,3)
y = 9x + 1
3x + 8y = 12
No, because when you plug the coordinates in for x and y, the equations are not true; 3 does not equal 1, and 24 does not equal 12.
55 people went on a school field trip. The number of children was 20 more than twice the number of teachers. Let c represent the number of children and let t represent the number of teachers who went on the trip.
c + t = 55
c = 2t + 20
This is the solution to the following system of equations:
x - 2y = -7
x - y = -4
X = -1
Y = 3