Facts of Systems
How Many Solutions?
What is the Next Step?
Substitution
Elimination
100
How many equations are in a system of linear equations?
2 equations
100
What are the three possible solutions we have learned for a System of Linear Equations?
One solution, No solutions, Infinitely Many Solutions
100
What is the next step?
2x=4
Divide by 2 on each side
100
Solve this System of Linear Equations using Substitution...TAKE YOUR TIME!!
y=5
y=3x+8
x=-1
y=5
Final Answer: (-1, 5)
100
Solve this System of Linear Equations using Elimination...TAKE YOUR TIME!!
x + 2y = 5
x + y = 2
x = -1
y = 3
Final Answer: (-1, 3)
200
What is the goal when solving a System of Linear Equations?
To find the value of both variables in the system
200
How many solutions are there in this System of Linear Equations?
1 solution
200
What is the next step?
3x-9=3
Add 9 to both sides
200
Solve this System of Linear Equations using Substitution...TAKE YOUR TIME!!
y=5x+2
y=2x+8
x = 2
y = 12
Final Answer: (2, 12)
200
Solve this System of Linear Equations using Elimination...TAKE YOUR TIME!!
4x + 2y = 10
2x + 2y = 12
x = -1
y = 7
Final Answer: (-1, 7)
300
How can we tell that our equations are linear?
They have an exponent of 1, or in other words, they don't have an exponent that we can see
300
How many solutions are in this System of Linear Equations?
y=3x-8
y=3x+4
No Solutions
300
What is the next step?
3x+6+4x=-1
Combine the variable terms because they are like terms. (3x+4x)
300
Solve this System of Linear Equations using Substitution...TAKE YOUR TIME!!
x + y = 4
2x + 4y = 6
x = 5
y = -1
Final Answer: (5, -1)
300
Solve this System of Linear Equations using Elimination...TAKE YOUR TIME!!
6x + 8y = 14
6x + 13y = 19
x = 1
y = 1
Final Answer: (1, 1)
400
What are the three methods we learned to solve a system of linear equations?
Graphing, Substitution, Elimination
400
How many solutions are in this System of Linear Equations?
y=
-19x+8
y=19x+8
1 Solution
400
What is the next step?
y=3x+4
y+2x=8
Substitute 3x+4 in for Y in the second equation
400
Solve this System of Linear Equations using Substitution...TAKE YOUR TIME!!
x - 3y = -14
3x + y = 8
x = 1
y = 5
Final Answer: (1, 5)
400
Solve this System of Linear Equations using Elimination...TAKE YOUR TIME!!
3x + 2y = 9
2x + 6y = 6
x = 3
y = 0
Final Answer: (3, 0)
500
When you solve a System of Linear Equations, what should our answer look like?
(x, y)
500
How many solutions are in this system of linear equations?
2 solutions
500
What is the next step?
3x-8y=37
3x+6y=9
Subtract the equations to eliminate the X variable
500
Solve this System of Linear Equations using Substitution...TAKE YOUR TIME!!
2x - y = 6
3x + 7y = 9
x = 3
y = 0
Final Answer: (3, 0)
500
Solve this System of Linear Equations using Elimination...TAKE YOUR TIME!!
-x + 5y = 8
3x + 7y = -2
x = -3
y = 1
Final Answer: (-3, 1)