Vocabulary
Any ordered pair that makes all equations in the system true is a _____________?
Solution
Write each equation in slope-intercept form. (y=mx+b).
y+2x=6
y - 8=-2x
y=-2x+6
y=-2x+8
When graphing a line, what is the first point that you need to graph?
y-intercept
Which equation should I always choose to manipulate first?
The more simple one.
What can I do with the two equations to help me eliminate?
Add/ Subtract/ Multiply
A __________________________ is formed by two or more linear equations that use the same variables.
System of equations
How many solutions does the system of equations have?
y+2x=6
y - 8=-2x
No solutions
Graph the system and determine its solution.
y=x+4
y=-2x+1
The point of intersection is (-1,3). Which means that the solution is (-1, 3).
Use substitution to solve.
-3y=-2x -1
y= x - 1
(4,3)_
Use elimination to solve.
2x -9y = -5
4x -6y = 2
(2,1)
Describe how you can find the number of solutions of two or more equations by using the slope and the y-intercept. (2-3 sentences)
Two or more linear equations that use the same variables are called a system of linear equations.
To find the solution of a system of linear equations, you can use the slopes and the y-intercepts. Same slope, different y-intercept means no solution. Same slopes, same y-intercepts means infinitely many solutions. Different slopes means one solution.
Determine whether the system of equations has one solution, no solution, or infinitely many solutions.
y - 13=5x
y - 5x=12
No solutions
Graph and find the solution(s).
y=1/2x+1
-2x+4y=4
Infinitely many solutions.
(Same slope, Same y-intercept, Same line).
Use substitution to solve.
y=5x+2
2y - 4= 10x
Infinitely many solutions
Use elimination to solve.
-2x +2y =2
4x -4y =4
No solution.
What is the mathematical difference between substitution and elimination when solving?
With substitution you plug in an expression to find the first variable. In elimination, you cancel out a variable to solve for the other variable first.
Determine whether the system of equations has one solution, no solution, or infinitely many solutions.
y=2x+10
3y - 6x=30
Infinitely Many
Graph and find the solution(s).
y= -x - 3
y+x=2
No solution
(Parallel lines)
(same slope, different y-intercept)
Use substitution to solve.
2y - 8 =6x
y=3x+2
No solution
Use elimination to solve each system.
4x +6y =40
-2x +y =4
(1,6)
What does it mean to solve a system of equations? (2-3 sentences)
Solving a system of linear equations means finding all of the ordered pairs that make the equations true.
Determine whether the system of equations has one solution, no solution, or infinitely many solutions.
y - 1/4x= -1
y - 2=4x
One Solution
Graph and find solution(s).
2y=6x+4
y=-2x+2
(0,2) One Solution
Use substitution to solve.
2y - 2=4x
y= -x+4
(1,3)
Use elimination to solve.
A customer at a concession stand bought 2 boxes of popcorn and 3 drinks for $12. Another customer bought 3 boxes of popcorn and 5 drinks for $19. How much does a box of popcorn cost? How much does a drink cost?
Box of popcorn: $3
Drink: $2