Solving Equations
−(7 − 4x) = 9
x = 4
4 + n/3 < 6
n < 6
Write the slope-intercept form of the equation of the line.
5x + 7y = 49
y = - 5/7 x + 7
Solve the system by graphing (find the point of intersection of the two lines).
y = - 1/4 x + 3
y = - 3/2 x - 2
(-4, 4)
Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?
$2
p − 1 = 5p + 3p − 8
p = 1
-4(3 + n) > -32
n < 5
Graph 2x − y = 3
The line will have a slope = 2 and y-intercept = -3.
Solve each system by substitution.
y = −3x + 5
5x − 4y = −3
(1, 2)
A number plus itself, plus twice itself, plus 4 times itself, is equal to − 104. What is the number?
− 13
24a − 22 = −4(1 − 6a)
No Solution
6 - 4(6n + 7) > 122
n < -6
Write the slope-intercept form of the equation of the line through the given point with the given slope. through: (3, 3), slope = 2
y = 2x - 3
Solve the system using the elimination method.
x + y = 1
-x + y = 5
(-2, 3)
Fourteen less than eight times a number is three more than four times the number. What is the number?
17/4
Mark spent $14 on a magazine and some notepads. If the magazine cost $5 and each notepad cost $3, then how many notepads did he buy?
3 notepads
Rich has $60 at most to spend on clothes. He wants to buy a pair of jeans for $22 and spend the rest on T-shirts. Each shirt costs $8. How many T-shirts can he buy?
4 T-shirts
Write the slope-intercept form of the equation of the line described.
through: (-2, 4), parallel to y = - 7/2x + 4
y = - 7/2x - 3
Solve the system by using the elimination method.
3x + 2y = 8
4x - 3y = -12
(4, 0)
At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. Which pair of equations can be used to determine t, the cost of a taco, and m, the cost of a small glass of milk?
t + m = 2.10
2t + 3m = 5.15
For a field trip 20 students rode in cars and the rest filled nine buses. How many students were in each bus if 236 students were on the trip?
24 students
A school has a budget of $240 per class to buy books. A math workbook costs $10 and a science workbook costs $12. If you buy 12 math workbooks, what is the maximum number of science workbooks you can buy?
We are given the number of math workbooks.
Let s = science workbooks.
12($10) + $12s ≤ $240
120 + 12s ≤ 240
12s ≤ 120
s ≤10
The school can buy 10 science workbooks.
Write the slope-intercept form of the equation of the line described.
through: (4, 4), perpendicular to y = -4/5x + 5
y = 5/4x - 1
The school that Kim goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
senior citizen ticket: $8, child ticket: $14
Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. For what number of shirts would the cost be the same?
12