Solving Systems of Equations
What is the difference between a linear equation and a system of linear of equations?
System = more than 1 equation
You might determine that graphing is our best method for solving if you see the two equations written in what "form" ?
Slope-intercept form
You might determine that substitution is our best method for solving if you see what kind of variable?
Isolated (variable)
If two variable terms have the same coefficient but opposite signs (+ or -) then you should use what operation to eliminate them?
Addition
How do you spell your teacher's NEW (married) last name?
S c h a f e r
If your system of equations has one unique solution, how do we write our final answer/solution?
Ordered pair
(x,y)
If you are graphing systems of equations and end up with one solution, what kind of lines would you expect to see on the coordinate plane?
Intersecting Lines
Solve the following system of equations:
y= -2
4x-3y=18
(3,-2)
If two variable terms have the same coefficient AND the same signs (+ or -) then you should use what operation to eliminate them?
Subtraction
Without even graphing, what can you look at with the equations to determine if a system has no solution?
Compare their slopes
If your system of equations has no solution, what terminology do we use to name or classify this type of system? (Hint: it starts with an "i")
Inconsistent
If you are graphing systems of equations and end up with no solution, what kind of lines would you expect to see on the coordinate plane?
Parallel Lines
Solve the following system of equations:
-3x-8y=20
y=5x+19
(-4,-1)
Solve the following system of equations:
-3x-4y=2
3x+3y= -3
(-2,1)
Show an example that compares an isolated variable versus a NON isolated variable.
x=4
versus
x+2y=5
If your system of equations has one unique solution, what terminology do we use to name or classify this type of system? (Hint: there are 2 words)
Consistent & Independent
If you are graphing systems of equations and end up with infinitely many solutions, what kind of lines would you expect to see on the coordinate plane?
Overlapping (coinciding) Lines
Solve the following system of equations:
y=5x-7
-3x-2y= -12
(2,3)
Solve the following system of equations:
-4x-2y= -12
4x+8y= -24
(6,-6)
Write a system of equations for the following written words:
Two times a number plus three times another number equals 13.
The sum of the two numbers is 7.
2x+3y=13
x+y=7
If your system of equations has infinitely many solutions, what terminology do we use to name or classify this type of system? (Hint: there are 2 words)
Consistent & Dependent
Solve the the following system of equations by graphing:
y= 2x+8
y=2x-1
No Solution
Solve the following system of equations:
-7x-2y= -13
x-2y=11
(3,-4)
Solve the following system of equations:
16x-10y=10
-8x-6y=6
(0,-1)
Write AND solve a system of equations for the following written words:
The sum of two numbers is 28 and their difference is 4. What are the numbers?
x+y=28
x-y=4
16 and 12