Solve by Graphing
Steps in Substitution
Solve by Substitution
How Many Solutions?
100
14) What is the solution to the system of linear equations?
(2,2)
100
If we were to do substitution and also have a graph of the same system of equations, would we get the same solution? Explain why.
Yes.
Every equation graphs a specific line so no matter how you solve, you get the same solution!
100
Solve the systems of equations using substitution:
y=3x-10
x=2
(2,-4)
100
How many solutions does the system of linear equations have?
One
200
What is the solution?
(-1,1)
200
What is the first step when solving a system of linear equations using the SUBSTITUTION method?
Make sure one equation says x= or y=
200
Solve the systems of equations using substitution:
y = -2x - 9
3x -6y = 9
(-3, -3)
200
How many solutions does the system of linear equations have?
y = 3x - 5
y = 3x + 7
Zero or None
300
Solve the system by graphing:
(-3, -3)
300
What is the second step in the substitution method? What is your new (one) equation after performing substitution?
y=2x
3x+y=20
Substitute the first equation into the second equation
3x+(2x)=20 or
5x=20
300
Solve the systems of equations using substitution:
y=2x-10
y=4x+8
(-9,-28)
300
How many solutions does the system of linear equations have?
y = (-5/3)x + 3
y = (1/3)x - 3
One
400
Solve the systems of linear equations by graphing:
(-4, -3)
400
What is the third step in the substitution method? What will the variable x equal in the system below?
y=2x
3x+y=20
Solve for one the variables
x=4
400
Solve the systems of equations using substitution:
2x - y = 6
x = y + 5
(1, -4)
400
How many solutions does the system of linear equations have?
y = 3x + 9
2y = 6x + 18
Infinitely many solutions
500
Solve this by graphing:
y = -2x+ 4
2y = -4x+8
Infinite Solutions
500
Use all four steps in the substitution method to solve the system of linear equations:
y=2x
3x+y=20
Solution: (4,8)
500
Use the substitution method to solve the system of linear equations:
6x + 2y = 12
y=-3x+8
No solution
500
How many solutions does the system of linear equations have?
y = 2x - 5
4y = 8x - 5
Zero or None