Equations
-3 + 2x = 11
x = 7
3 ⋅ 8
24
Solve the system Substitution:
y = 5x
2x + 2y = 24
(2, 10)
The cost of using a telephone in a hotel meeting room is a flat fee of $5 plus $0.20 per minute. What equation represents the total cost, c, in dollars, for m, minutes of phone use?
c = 5 + 0.20m
If y = 4, simplify the expression:
8y - 2x
32 - 2x
4x + 6 = -10
x = -4
4 ⋅ –9
-36
Solve the system Elimination:
6x - 4y = 3
3x - 4y = -1
(5, 4)
A website-hosting service charges businesses a onetime setup fee of $350 plus d dollars for each month. A business owner paid $1,010 for the first 12 months, including the setup fee. What equations fits this scenario?
350 + 12d = 1,010
If x = 3 + y, solve for y:
9x = 7y + 6
y = -21/2
x + 9 = 18 - 2x
x = 3
–5 ⋅ –7
35
Solve the system:
x - 4y = -19
3y - 15 = x
(-3, 4)
$7.99 is two dollars less than three-fourths of the money in Hector’s pocket. Write an equation to illustrate this scenario.
(3/4)x – 2 = 7.99
Simplify: (½) a + 3ab – (½) a + b + 7
3ab + b + 7
2x + 6 = 4x - 2
x = 4
–6 ⋅ 11
-66
Solve the system:
y - 2x = -1
4x - 2y = 2
System has No Solution
A babysitter earns $8 an hour for babysitting 2 children and an additional $3 tip when both children are put to bed on time. If the babysitter gets the children to bed on time, what expression could be used to determine how much the babysitter earned?
8x + 3, where x is the number of hours
-5[4 – 3(2 – 5x)] = -75x + 10
All possible solutions
-x - 1 = 221 + 2x
x = -74
Explain why –2 ⋅ 4 = –8
Because a negative number multiplied by a positive number gives a negative answer, and 2 ⋅ 4 = 8
Solve the System:
3y = 2x + 5
2x + y = -9
(-4, -1)
A grocery store sells a brand of juice in individual bottles and in pack of 6 bottles. On a certain day, the store sold a total of 281 bottles of the brand of juice, of which 29 were sold as individual bottles. Which equation shows the number of packs of bottles, p, sold that day?
p = (281 – 29)/6
What is the value of 3x,
if 9x = 5y + 2 and y + 4 = 2y -10?
3x = 24