Substitution
Solve
y = 10x
y = -3x + 39
(3, 30)
Solve
9x - 9y = -9
3x + 9y = -15
(-2, -1)
Noah went into a movie theater and bought 9 drinks and 4 candies, costing a total of $60. Nachelle went into the same movie theater and bought 10 drinks and 2 candies, costing a total of $57.50. Determine the price of each drink and the price of each candy.
Each drink costs $5 and each candy costs $3.75.
Use desmos and determine the number of solutions in the system
2x + y = 5
-8x - 4y = -20
infinitely many solutions
Solve
y = -6x
-2x - 7y = 40
(1, -6)
Solve
-8x + 5y = 43
-8x + 4y = 36
(-1, 7)
Malik and his children went into a grocery store and he bought $28 worth of apples and mangos. Each apple costs $1.75 and each mango costs $2. He bought a total of 15 apples and mangos altogether. Determine the number of apples and the number of mangos that Malik bought.
Malik bought 8 apples and 7 mangos.
Use desmos and determine the number of solutions in the system
-5x + y = 7
5x - y = -5
no solutions
Solve
3x + y = 20
x = -7y
(7, -1)
Solve
2x + 4y = -14
x - 2y = 9
(1, -4)
Joseph has $1.45 worth of nickels and dimes. He has a total of 17 nickels and dimes altogether. Determine the number of nickels and the number of dimes that Joseph has.
There are 5 nickels and 12 dimes.
Use desmos and determine the number of solutions in the system
-x + y = -6
3x - y = 5
one solution
Solve
y = -7x + 10
3x + 2y = 9
(1, 3)
Solve
5x - 4y = 34
-x + 8y = 22
(10, 4)
Elijah has $1.60 worth of nickels and dimes. He has 5 more nickels than dimes. Determine the number of nickels and the number of dimes that Elijah has.
There are 14 nickels and 9 dimes.
Use desmos and determine the number of solutions in the system
-2x + y = -3
6x - 3y = 7
no solution
Solve
8x - 5y = 37
x = 2y + 6
(4, -1)
Solve
-3x - 5y = 45
2x - 2y = 2
(-5, -6)
Jordan is working two summer jobs, making $13 per hour lifeguarding and $10 per hour walking dogs. Last week Jordan earned a total of $177 and worked 3 more hours lifeguarding than hours walking dogs. Determine the number of hours Jordan worked lifeguarding last week and the number of hours he worked walking dogs last week.
Jordan worked 9 hours lifeguarding and 6 hours walking dogs.
Use desmos and determine the number of solutions in the system
-3x + y = -5
-6x + 2y = -10
infinitely many solutions