Solve It!
Solve: 5x+7=2x+22
x=5
Classify: 3(x + 2) = 3x + 6
Solve if one solution
Infinitely many solutions
What does the solution to a system of two linear equations represent on a graph?
The point where the two lines intersect.
Solve: y = x + 2 and y = 10 - x
(4, 6)
Solve: x + y = 9 and x - y = 3
(6, 3)
Solve: 3(x+4)+2x=27
x=3
Classify: 5(x - 1) = 5x + 4
Solve if one solution
No solution
Check whether (2, 3) is a solution to y = x + 1 and y = -x + 5.
Yes
Solve: y = 2x + 1 and x + y = 7
(2, 5)
Solve: 3x + 2y = 16 and 3x - 2y = 8
(4, 2)
Solve: 6−2(3x−1)=4x+18
x=−1
Classify: 4x + 9 = 2x + 17
Solve if one solution
One solution; x = 4
Solve by graphing: y = x + 1 and y = -x + 5
(2, 3)
Solve: x = y + 2 and 2x + y = 13
(5, 3)
Solve: 2x + 3y = 12 and x - y = 1
(3, 2)
x/3 + 5 = 2x/5 - 1
x=90
Find a and b so ax + 12 = 5x + b has infinitely many solutions.
a = 5, b = 12
Solve by graphing: y = 2x - 1 and y = -x + 5
(2, 3)
Solve: y = 3x - 5 and 2x + y = 9
(14/5, 17/5)
Adult tickets cost $8 and student tickets cost $5. A total of 30 tickets were sold for $201. How many of each were sold?
17 adult tickets and 13 student tickets
Solve: 4(2x−3)−3(x+5)=2(x−7)+5x
No solution
Find a and b so a(x + 3) + 2x = 5x + b has infinitely many solutions.
a = 3, b = 9
Solve by graphing: y = 3x - 4 and y = -(2/3)x + 4/3
About (1.45, 0.36)
Solve: x = -(1/4)y + 8 and x = 5y - 13
(4, 16)
A boat travels 24 miles downstream in 2 hours and the same distance upstream in 3 hours. Find the boat's speed in still water and the current's speed.
Boat = 10 mph, Current = 2 mph