Solve by Graphing
y=x+3
y= 2/ 5 x
(-5,-2)
x = -7
4x + 6y = -4
(-7,4)
How many solutions would a system of linear equations have if the equations are parallel and different y-intercepts?
Zero Solutions
What is the slope of this equation?
y = -1/2 x +7
-1/2
How many solutions?
y-13=5x
y-5x=12
No Solution
Solve this by graphing:
y = 2x - 4
y = -1/3 x + 3
(3,2)
3x + 7y = 14
x - 3y = -6
(0,2)
How many solutions would a system of linear equations have if the equations are parallel and have the same y-intercept?
Infinite Solutions
In the form y = mx + b
What do m and b represent?
m = slope
b = y-intercept
How many Solutions?
y-1/4x=-1
y-2=4x
One Solution
x-4y=-12
3x+2y=-8
(-4,2)
y=2x-10
y=4x+8
(-9,-28)
Is there 1 solution, No solution, or Infinite solutions for the following question?
y = -3x -19
y = -3x+ 10
No Solutions
What is the y-intercept of this equation?
-24=9x+6y
(0,-4)
What is the solution to this system? Solve by graphing
y=1/2x+1
-2x+4y=4
Infinitely Many Solutions
3y=x-12
-x+3y=-12
Infinite number of solutions as lines coincide
x + y = 10
–x − 3y = –14
(8, 2)
How many solutions does the system have?
3y + 4x = 6
12y + 16x = 24
These are the same exact line, therefore they have
Infinite Solutions
What is true of lines with no solution?
They are parallel
What is the solution to this system? Solve by graphing
2y=6x+4
y=-2x+2
(0, 2)
Solve the systems of linear equations by graphing:
y = x+4
y = -5x-2
(-1,3)
Solve the systems of equations using substitution:
-8x + y = -7
16x - 2y = 14
Infinitely Many Solutions as lines coincide
How many solutions does the system have?
y= -4x+7
y = x+2
Different slopes,
One solution
What does it mean if a system of equations has infinite solutions?
They are the same line -- Lines coincide
Use substitution to solve each system.
y=5x+2
2y-4=10x
Infinitely Many Solutions