Describe for me...
Describe what it means when a system of equations has one solution.
The lines are intersecting
Graph the equation y = 2/3 x + 3
y-intercept: 3
slope: 2/3 ; rise: 2, run 3
y = x + 1
2x + y = 4
(1,2)
3x + y = 5
-x -y = 1
(3, -4)
-4x - 2y = -8
y= 2x + 4
Describe what it means when a system of equations has no solution
The lines are parallel
Graph the equation y = -3 x - 5
y-intercept: -5
slope: -3; rise -3, run 1
x - y = -2
7x + 2y = -5
( -1, 1)
x - y= -10
x - 6y = -25
(-7,3)
2x + 5y = -7
7x + y = -8
(-1, -1)
Describe what it means when a system of equations has infinite solutions
The lines are the same
Graph the equation x + y = 3
slope: -1
y-intercept: 3
y= -5
8x + 5y = -17
(1, -5)
2x + 2y = 28
8x - 2y = 22
(5,9)
x - 3y = -24
5x + 8y = -5
( -9, 5)
Name the three types of solutions for a system of equations
One Solution, Infinite Solution, No Solution
Graph the equation x + 2y = -6
slope: -1/2
y-intercept: -3
8x + 5y = -13
3x + 4y = 10
(-6, 7)
3x + 6y = 27
x + 2y = 11
No Solution
x + 2y = 3
5x + 3y = 8
(1,1)
Name the three methods of solving a system of equations
Graphing, Substitution, Elimination
Graph the equation 3x - y = 7
y-intercept: -7
slope: 3
x - 7y = -21
2x - 14y = -42
Infinite Solutions
4x + 5y = 22
7x - 3y = -32
(-2, 6)
2x = 8y - 2
3x - 3y = 15
(7, 2)