What will the graph look like for a system of equations that has no solution?
Responses
The lines will be perpendicular
The lines will cross at one point
Both equations will form the same line
The lines will be parallel.
The lines will be parallel.
The point (5, −3)
is a solution to which system of equations?
Responses
y=x−8
2x+y=7
y is equal to x minus 8, , 2 x plus y is equal to 7,
y = x + 2
y = x + 5
y = x + 2
, , y = x + 5
,
y = −12x + 6
y = 3x − 1
y = −12x + 6
, , y = 3x − 1
,
y = 23x + 6
3y + 6x − 18 = 0
y=x−8
How many solutions does the system of equations have?
y = −2x +12
4y + x −20 = 0
Responses
No Solution
No Solution
Infinitely many solutions
Infinitely many solutions
One solution
One solution
Two solutions
One solution.
A company owns two dealerships, both of which sell cars and trucks. The first dealership sells a total of 164 cars and trucks. The second dealership sells twice as many cars and half as many trucks as the first dealership, and sells a total of 229 cars and trucks.
An equation for the total cars and trucks for dealership A:
An equation for the total cars and trucks for dealership B:
How many cars did dealership A sell?
How many trucks did the dealership B sell?
Equation for dealership A:
cars + trucks = 164
Equation for dealership B:
2(cars) + 0.5(trucks) = 229
To find how many cars dealership A sold, we need to solve for cars in the equation for dealership A:
cars = 164 - trucks
To find how many trucks dealership B sold, we can use the equation for dealership B:
0.5(trucks) = 229 - 2(cars)
trucks = (229 - 2(cars))/0.5
Substituting the equation for cars in terms of trucks from dealership A into this equation and simplifying:
trucks = 229 - 2(164 - trucks)
trucks = 101
So dealership A sold 63 cars (164 - 101) and dealership B sold 101 trucks.
The sum of two numbers is 22. Three times one number increased by five is 35. What are the two numbers?
Responses
11
11
10
10
6
6
15
15
7
7
12
12
16
10 and 12.
At Barnes and Noble, Sylvia purchased a journal and a cookbook that cost a total of $54, not including tax. If the price of the journal, j, is $3 more than 2 times the price of the cookbook, c, which system of linear equations could be used to determine the price of each item?
1. The equation for the total cost
2. The equation for the price of the journal
3. You can choose any method to solve this system: graphing, substitution, or elimination. Choose a method and solve for the price of the journal and the cookbook.
The price of the journal is
The price of the cookbook is
1. j + c = 54
2. j = 2c + 3
We can use substitution method to solve for j and c:
j + c = 54
j = 2c + 3
Substitute the second equation into the first equation:
2c + 3 + c = 54
3c = 51
c = 17
Substitute the value of c into the equation for j:
j = 2c + 3
j = 2(17) + 3
j = 37
Therefore, the price of the journal is $37 and the price of the cookbook is $17.
Samuel currently has 18 rocks in his collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week.
Set up a system of equations to show how many rocks each has in their collection.
Samuel has y=Response areax+Response area.
Lewis has Response areax+Response area.
After how many weeks will Samuel and Lewis have the same number of rocks in their collections? Response area weeks
How many rocks will Samuel and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection.
Samuel has y = 18 + 4x, where x is the number of weeks
Lewis has y = 30 + 3x, where x is the number of weeks
To find when they will have the same number of rocks in their collections, we can set the two equations equal to each other and solve for x:
18 + 4x = 30 + 3x
x = 12
So after 12 weeks, Samuel and Lewis will have the same number of rocks in their collections.
To find how many rocks they will each have at that time, we can substitute x = 12 into either equation:
Samuel: y = 18 + 4x = 18 + 4(12) = 66 rocks
Lewis: y = 30 + 3x = 30 + 3(12) = 66 rocks
Therefore, when they have the same number of rocks in their collections, they will each have 66 rocks.
Which graph represents the solution for the equation -5/2x -1 = 4x +2
Responses
There are no graphs provided as options to choose from. Please provide the graphs for me to determine which one represents the solution for the given equation.
Billy is 6 years younger than Amy. The sum of their ages is 22. How old will each of them be in 8 years?
Amy will be Response area and Billy will be
Let's represent Amy's age as A and Billy's age as B.
From the first piece of information, we know that:
B = A - 6
From the second piece of information, we know that:
A + B = 22
We can use substitution to solve for A:
A + (A - 6) = 22
2A - 6 = 22
2A = 28
A = 14
So Amy is currently 14 years old, and Billy is:
B = A - 6 = 14 - 6 = 8
In 8 years, Amy will be 22 years old (14 + 8), and Billy will be 16 years old (8 + 8).
Solve the system of equations
3x+2y=2
−2x+y=8
Responses
(-4,2)
(-4,2)
(4,-2)
(4,-2)
(-2,4)
(-2,4)
(14,-20)
(-4,2)
Not including tax, a total of 19 pens and markers cost $11.50. The pens cost $0.25 each, and the markers cost $0.75 each. Write the system of equations that could be used to solve for the number of pens (p) and the number of markers (m) bought.
p+m=Response area
Response areap+ Response aream=
p + m = 19
0.25p + 0.75m = 11.50 (since the pens cost $0.25 and the markers cost $0.75)
Therefore, the system of equations that could be used to solve for the number of pens and markers bought is:
p + m = 19
0.25p + 0.75m = 11.50
Joyce wants to mix granola and raisins together to make a snack for her class. Granola costs $2 per pound and raisins cost $4.50 per pound. Joyce is willing to spend $37.50 and wants to make 15 pounds of trail mix.
g+Response area=15
2Response area+4.5r=
g + r = 15
2g + 4.5r = 37.5
where g is the weight (in pounds) of granola, and r is the weight (in pounds) of raisins.
The first equation represents the fact that she wants to make 15 pounds total. The second equation represents the fact that the cost of the granola and raisins combined cannot exceed $37.50. The cost of the granola is $2 per pound, and the cost of the raisins is $4.50 per pound.
Note that there are multiple ways to set up this system of equations. For example, you could also write:
2g + 4.5r = 37.5 (total cost cannot exceed $37.50)
g + r = 15 (total weight must be 15 pounds)
Michelle bought some potted plants.
Petunias cost $7 per pot.
Begonias cost $8 per pot.
She bought 22 potted plants and spent a total of $163. How many petunias did she buy?
Responses
7
7
9
9
11
11
14
14
13
We can set up a system of linear equations to solve the problem. Let p be the number of petunias and b be the number of begonias:
p + b = 22 (she bought a total of 22 potted plants)
7p + 8b = 163 (she spent a total of $163)
We can use substitution to solve for one of the variables, say b, in terms of the other:
b = 22 - p (substitute into the second equation)
7p + 8(22 - p) = 163 (solve for p)
7p + 176 - 8p = 163
-p + 176 = 163
-p = -13
p = 13
Therefore, Michelle bought 13 petunias.