All about Systems of Equations
Solving Systems of Linear Equations: Graphing
Solving Systems of Linear Equations: Substitution1
Solving Systems of Linear Equations: Substitution2
100
What is a the slope-intercept form of linear equation?
y=mx+b
100
14) What is the solution to the system of linear equations?
(2,2)
100
If we were to do substitution and have a graph of the same system of equations would we get the same solution?
Yes.
Every equation graphs a specific line so no matter how you solve, you get the same solution!
(Graphs are definitely easier, but we don't always have graphed systems!)
100
Solve the systems of equations using substitution:
y=3x-10
x=2
(2,-4)
200
True or False:
It does not matter which method you use when solving systems of linear equations because they will all give you the same answer.
True
200
What is the solution?
(-1,1)
200
What is the first step when solving a system of linear equations using the SUBSTITUTION method?
Get one of the variables by itself in one of the equations.
200
Solve the systems of equations using substitution:
y=2x-10
y=4x+8
(-9,-28)
300
What does it mean to "find the solution" to a system of linear equations?
It means to find the point where the two lines intersect (cross)
300
If the graph of a linear system of linear equations is two parallel lines, how many solutions are there? Explain.
There are no solutions because the two lines do not cross.
300
What is your new (one) equation after performing substitution?
y=2x
3x+y=20
3x+(2x)=20 or
5x=20
300
Solve the systems of equations using substitution:
y = -2x - 9
3x -6y = 9
(-3, -3)
400
What is a system of equations?
2 or more equations
400
Identify the slope and y-intercept of each of the equations.
Equation1: Slope is 1/4 and y-intercept is -2
Equation2: Slope is 3/2 and y-intercept is 3.
400
How would you isolate x in this equation?
6y+x=20
subtract 6x from both sides to get:
x=20-6x
400
Solve the systems of equations using substitution:
2x - y = 6
x = y + 5
(1, -4)
500
What are the 3 methods we use to solve systems of linear equations?
Graphing, Substitution, Elimination
500
To eliminate the "y", what must be done to the first equation and why?
2x - y = 4
x + 3y = 3
The first equation needs to be multiplied by 3 to have opposite coefficients.
500
Use the substitution method to solve the system of linear equations:
y=2x
3x+y=20
Solution: (4,8)
500
Use the Elimination method to solve the system of linear equations:
−8x − 10y = 24
6x + 5y = 2
(7,-8)