Systems of Equations
Solve for x and y:
2x+y=5
-3x+6y=0
(2,1)
Equivalent equations
a. have the same denominator
b. have the same number of terms
c. have the same solution
d. can only be written one way
c. have the same solution
An old man buys books and dog toys with his spending money. He budgets 90 dollars per month for these items. The books he reads cost $6 and the dog toys cost $3. An equations showing this budget is:
90= 6x+3y
If he buys 3 books, how many dog toys can he get?
24
A yearbook costs $12. Each additional portrait of your teachers costs $8. Extra signing pages cost $0.50.
Write an equation that represents the total cost of a yearbook.
C = 8T +0.5P + 12
Two numbers have a sum of 10, but their product is 16. What are they?
2 and 8
The solution to a system of equations problem is:
a. an even number
b. always a line
c. an ordered pair
c. an ordered pair
True or False:
3x-5= 19 and 3x+30=6 are equivalent.
False: Their solution are 8 and -8, respectively
An old man buys books and dog toys with his spending money. He budgets 90 dollars per month for these items. The books he reads cost $6 and the dog toys cost $3. An equations showing this budget is:
90= 6x+3y
If he only buys books, how many can he get?
15 books
Dr. King (One of Mr. Swissdorf's dogs) can go to daycare for $24 per day. He can get meals for $2.00. Extra play time costs $5 per period. Write an equation for dog daycare so Mr. Swissdorf realizes how expensive pets are.
C = 2m + 5p + 24
A gardener has 50 feet of fence but she wants the width of her rectangular garden to be 5 feet wide. How long can her garden be?
a. 45 feet
b. 20 feet
c. 22.5 feet
c. 22.5 feet
We can perform any operation on an equation in a system as long as
a. we have permission
b. we multiply by zero
c. we can reverse the operation
c. we can reverse the operation
True or false:
3/2x + 3 =3 -(4x+12) and 3x + 6 = -8x -18 are equivalent
True
An old man buys books and dog toys with his spending money. He budgets 90 dollars per month for these items. The books he reads cost $6 and the dog toys cost $3. An equations showing this budget is:
90= 6x+3y
If he only buys dog toys, how many could he get?
30 toys
Ronaldo gets $245 million a year (really). He also gets bonuses for scoring goals of about 2 million (that's real, but the number is fake to make the problem easier). Additionally he gets a second bonus for being nice and really pretty. Every time he smiles he gets 3 million.
Write an equation for how freaking rich Ronaldo is
T = 245+ 2g+ 3n
Ethane, propane and pentane have the following chemical formulas: C2H6, C3H8, C5H12 Use the pattern in the formulas to determine how many hydrogen atoms (H) would bond with 8 carbons (C).
a. 8 b. 12 c. 14 d. 16 e. 18
e. 18
Solve for x and y:
2x-3y=9
4x+2y=-22
(-3,-5)
True or False
2(2x-3) = 3(x-1)+6 and 4x-6 = 3x+3
True
An old man buys books and dog toys with his spending money. He budgets 90 dollars per month for these items. The books he reads cost $6 and the dog toys cost $3. An equations showing this budget is:
90= 6x+3y
How many books and toys could he buy if he wanted an equal number of books and toys?
10 books and 10 toys.
A woodworker gets 300 dollars a month, plus an additional payment for items that sell. Her earnings can be represented by the following equation:
E = 300 + (p) (i), where p is the payment amount and i is the number of items that sold.
What is the best equation we can use to find the number of items sold (if we know E and p).
i= e-300/p
Two sides of a right triangle are 8 and 6 meters. How long is the third side?
10 meters
Solve for x and y:
3x-5y=-13
4x+2y = 0
(-1,2)
are the following equations equivalent?
5x +6+3-(4x+12) and 5x +6 =-8x-18
Nope
An old man buys books and dog toys with his spending money. He budgets 90 dollars per month for these items. The books he reads cost $6 and the dog toys cost $3. An equations showing this budget is:
90= 6x+3y
Sketch a graph of the number of books and dog toys he can buy
See White Board
A woodworker gets 300 dollars a month, plus an additional payment for items that sell. Her earnings can be represented by the following equation:
E = 300 + (p) (i), where p is the payment amount and i is the number of items that sold.
What is the best equation we can use to find the payment amount (p) (if we know E and i)?
E-300/i = p
The product of two numbers is 24, but their sum is -11. What are they?
-3, and -8