Solve by Graphing
Identify the solution to the system of equations according to the graph.
y = -2x + 1
y = x - 2
[slide 24]
(1, -1)
Solve the system of equations by substitution.
x = 3y
x + 2y = 30
(3y) + 2y = 30 x = 3(6)
5y = 30 x = 18
y = 6
(18, 6)
Does this system of equations have infinitely many solutions or no solution?
y = 2x - 6
y = 2(x - 3)
Infinitely many solutions; they are the same line!
Identify the solution to the system of equations according to the graph.
y = -x + 1
y = x - 1
[slide 25]
(1, 0)
Solve the system of equations by substitution.
y = x + 1
x + y = 17
x + (x + 1) = 17 y = (8) + 1
x + x + 1 = 17 y = 9
2x + 1 = 17
2x = 16
x = 8
(8, 9)
Does this system of equations have infinitely many solutions or no solution?
x + y = 13
y = -x + 13
Infinitely many solutions; they are the same line!
Identify the solution to the system of equations.
y = -2x + 9
y = 5x + 9
(0, 9)
[Same y-intercept]
Solve the system of equations by substitution.
x + y = 12
x + 3y = 22
x + y = 12
x = 12 - y
(12 - y) + 3y = 22 x = 12 - (5)
12 - y + 3y = 22 x = 7
2y = 10
y = 5
(7, 5)
Does this system of equations have infinitely many solutions or no solution?
y = 2x - 6
y = 2(x + 3)
No solution; they are parallel!