Methods
Name two methods used to solve a systems of equations.
graphing
set =
elimination (addition, subtraction, multiplication)
substitution
When graphing a system of equations, the solution lies at the point of ______________?
intersection
substitute the known variable into the top equation and solve for the unknown variable
To use elimination with addition you need your x's or y's to be ___________.
opposites
The answer to a systems of linear equations.
solution
ordered pair
Which method would you use to solve this system of linear equations?
4x-3y=-2
2x-3y=6
elimination with subtraction
What does a system of linear equations with no solution look like on a graph?
parallel lines
To use the "set them equal" method both equations need to be in ______________.
slope-intercept form
3x+4y=12
3x-2y=14
elimination with subtraction or multiplication
How many solutions does a system have if the graph is a set of parallel lines?
none
How do you check your work when solving a system?
substitute the x- and y- values into both equations to see if they make true statements
no solution
The solution of the following system of equations:
y=-5+2x
y=6x+3
What is "(-2, -9)"?
Show your work to your teacher.
What is the goal when using the Elimination Method?
To make the x's or y's total 0.
The format used to write a solution of a system of linear equations.
ordered pair or (x,y)
Which method would you use to solve this system of linear equations?
y=-2x+3
y=4x+2
set =
elimination with subtraction
elimination with multiplication
How many solutions does a system have if the lines intersect at one point?
one
The solution of the following system of equations:
y=x-3
y=-2x+3
What is "(2, -1)"?
Show your work to your teacher.
The solution of the following system of equations:
3x-6y=3
4x+6y=32
What is "(5, 2)"?
Show your work to your teacher.
If the graph of a system of equations intersects twice, how many solutions does it have?
2
Which method would you use if you had a picture of the systems?
graphing method
To name the solution of a system of linear equations what would you use?
The solution of the following system of equations:
y=-3x
y=x
What is "(0, 0)"?
Show your work to your teacher.
What would you multiply the second equation by to eliminate the x's?
2x+8y=-22
x+5y=-12
2 or -2
When you subtract the equations below, what does the second equation become?
2x+3y=12
2x-4y=10
-2x+4y=-10