First-Degree
3x – 5 = 19
8
7t + 6= -2
-8/7
Find the value of two numbers if their sum is 12 and their difference is 4.
4 and 8
(k - 4)(k + 7) = 0
{4, -7}
7(x + 2)(x + 4) = 0
{-2, -4}
8x – 9 = 13x + 21
-6
40r + 15=22r - 3
-1
There are 13 animals in the farm. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?
6 chickens and 7 pigs
8x2 + 64x + 120 = 0
{-5, -3}
r2 - r - 30 = 0
{-5, 6}
5z – 7 = 7 - 5z
7/5
4(x - 3) - 3(x - 4) = 5(x + 2) + 6
-4
Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?
2 fancy shirts and 5 plain shirts
12k2 - 30k = 0
{ 5/2 , 0 }
35p2 - 30p = 0
{ 6/7 , 0 }
3y-[5-2(y+1)]=y-7(y+2)
-1
a(a-2)-15=a(a+5)-3(a+5)
0
A class of 195 students went on a field trip. They took 7 vehicles, some cars and some buses. Find the number of cars and the number of buses they took if each car holds 5 students and each bus hold 45 students.
3 cars and 4 buses
7x2 - 34x + 19 = -5
{ 6/7 , 4 }
6k2 - 35k + 2 = 8
{-1/6 , 6 }
7z - 3(4 - z) = 5(2z) + 12
no solution
Solve for y
2(x - y) = 3x + 4
-(x + 4 / 2)
A store sells handmade forks and spoons. It costs the store $1.70 to buy the supplies to make a fork and $1.30 to buy the supplies to make a spoon. The store sells forks for $5.60 and spoons for $5.40. Last April the store spent $37.90 on materials for forks and spoons. They sold the finished products for a total of $147.20. How many forks and how many spoons did they make last April?
7 forks and 20 spoons
3n2 + 9 = 12
{1, -1}
3k2 - 12 = 0
{2, -2}