Vocab
What does the term "substitution" mean?
Replacing a value for the value it holds
What's the error?
y=3x
2y+x=14
2(3x)+x=14
6x+x=14
7x=14
x=7
Math error
To solve a system of equations by substitution we need to get what by itself?
One variable ( x or y)
Solve the following by substitution
x=4y
x+y =10
(8,2)
What is the first step when solving a system of equations by substitution?
make sure you have an isolated variable
What's the error?
y=2x
x+y=9
2x + y = 9
3y = 9
y = 3
Substitution Error
Solve the systems of equations using substitution
x=-3
x - 3y=-15
(-3,4)
Solve the following by substitution
x= 5y
2x+3y = 26
(2, 10)
What does it mean for there to be infinite/many solutions?
Equations have the same slope and are the same exact line
What is the error?
y=5x
2x−y=3
2x - 5x = 3
3x = 3
x = 1
negative error
Solve the systems of equations using substitution:
y = 6x
2x + 3y=-20
(-1,-6)
Solve by Substitution
3x+3y = 12
y=4
(0,4)
What does it mean for there to be No Solution?
The two lines will never intersect
What's the error?
y = 2x
3x - 2y = 8
3x - 2(2x) = 14
3x + 4x = 14
7x = 14
x = 2
Sign Error
Solve the systems of equations using substitution:
x=4y
x+2y=12
(8,2)
Use Substitution to solve each system of equations.
y = 3x
3y + x = 50
(5, 15)
What is wrong with the following solved equation?
X= 6y
2x + 3y = 20
2x + 3(6x) = 20
2x + 18x = 20
20x = 20
x = 1
Substituted wrong
What's the error?
y=4x
2y+x=18
2 (4x) + 2x = 40
8x + 2x = 40
8x = 40
x = 5
Combine Like Terms Error
Use substitution to solve the following system of equations.
y = -2x + 3
8x + 4y =12
infinitely many solutions
Use Substituion to solve each system of equations.
2x + 1y = 10
y = -2x + 15
No Solution