Solving Equations
x = 7
How many solutions does this equation have?
2x + 3 = 3 + 2x
Infinite Solutions
Graphing the lines and seeing where they cross.
Solve this system of equations:
y = 5
y = 3x - 7
(4, 5)
Create an system of equation for these:
Jada bank offers an incentive for getting a savings account by giving new accounts $26 and Jada plans to save $7 each week after she opens her account.Andre's bank offers a similar incentive of $50 for new accounts and he plans to save $5 each week after he opens the account.
y = 7x + 26
y = 5x + 50
Solve for x:
2 (3x + 1) = 32
x = 5
How many solutions does this equation have?
7(x - 4) = 4x + 5
One Solution
How would you graph this line?
y = 2x - 5
Start at -5. Move by a slope of 2 (up 2, right 1)
y = 3x
y = 5x -2
Does this have a solution of (5, 2)
y = x - 3
y= -x + 3
NO.
x + 3 - 2x = 7 - 2x
x = 4
How many solutions does this equation have?
-6x = -6x - 1
NO Solution
What does a graph look like with no solutions?
Parallel Lines
y = 4x + 2
(6, 27)
When will Jada and Andre have the same amount money? How much money will they have?
Jada bank offers an incentive for getting a savings account by giving new accounts $26 and Jada plans to save $7 each week after she opens her account.Andre's bank offers a similar incentive of $50 for new accounts and he plans to save $5 each week after he opens the account.
12 weeks and $110
Solve for x:
3(2x - 1) - 10 = 8 + 5x
x = 21
How many solutions does this equation have?
2x + 3 = 2x + 5
No Solution
What does a graph look like if there is infinitely many solutions?
Two lines in the same location (on top of each other)
y = x - 3
y = -2x + 12
(5, 2)
Who has more money after 4 weeks of saving?
Jada bank offers an incentive for getting a savings account by giving new accounts $26 and Jada plans to save $7 each week after she opens her account.Andre's bank offers a similar incentive of $50 for new accounts and he plans to save $5 each week after he opens the account.
Andre
-2(3x +5) = 1/2 (-8x + 4)
x = -6
How many solutions does this equation have?
4 (x - 2) = 4x - 8
Infinite Solutions
graph these two equations:
y=2x+1
y=−x+7
Cross at (2, 5)
y = 2x + 1
2x + 2y = 14
(2, 5)
Is (4,3) a solution to this system?
y = x - 1
2x - y = 5
Yes