The point (5, −3)
is a solution to which system of equations?
Responses
y=x−8
The system of equations is not provided. Please provide the complete set of equations for me to determine which one the given point is a solution to.
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
The point (5, -3) is a solution to the system of equations:
y = x - 8
because when we substitute x = 5 and y = -3 into this equation, we get:
-3 = 5 - 8
which is true.
Match the system of equations graphed to the correct solution.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
I'm sorry, but I cannot see any system of equations or graphs attached to the question. Please provide more information or details.
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
The system of equations has only one solution.
Answer this with no mistakes
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.
Answer this with no mistakes
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 total cars and trucks at dealership A: x + y = 164, where x represents the number of cars and y represents the number of trucks sold at dealership A.
Equation for total cars and trucks at dealership B: 2x + 0.5y = 229, where x represents the number of cars and y represents the number of trucks sold at dealership B.
To find how many cars dealership A sold, we can use the first equation and solve for x: x + y = 164 → x = 164 - y.
To find how many trucks dealership B sold, we can use the second equation and solve for y: 2x + 0.5y = 229 → y = 458 - 4x. Then, we substitute the value of x from the first equation into the second equation: y = 458 - 4(164 - y) → y = 110.
Therefore, dealership A sold 164 - y = 164 - 110 = 54 cars, and dealership B sold y = 110 trucks.
The sum of two numbers is 22. Three times one number increased by five is 35. What are the two numbers?
Responses
16
16
7
7
10
10
6
6
15
15
11
11
12
The two numbers are 9 and 13.
Let x be the first number and y be the second number.
From the first sentence, we know that:
x + y = 22
From the second sentence, we know that:
3x + 5 = 35
Solving the second equation for x, we get:
3x = 30
x = 10
Substituting this value of x into the first equation, we get:
10 + y = 22
y = 12
Therefore, the two numbers are 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. Equation for the total cost:
j + c = 54
2. Equation for the price of the journal:
j = 2c + 3
To solve this system of equations, we can use the substitution method:
Substitute the second equation into the first equation:
(2c + 3) + c = 54
Simplify and solve for c:
3c + 3 = 54
3c = 51
c = 17
Then, we can substitute this value of c into the second equation to find the value of j:
j = 2(17) + 3 = 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.
The system of equations for the number of rocks in Samuel's and Lewis's collections can be set up as follows:
Samuel: y = 18 + 4x, where y is the total number of rocks in Samuel's collection and x is the number of weeks he has been collecting rocks.
Lewis: y = 30 + 3x, where y is the total number of rocks in Lewis's collection and x is the number of weeks he has been collecting rocks.
To find when Samuel and Lewis will have the same number of rocks, we can set the two equations equal to each other and solve for x:
18 + 4x = 30 + 3x
x = 12
Therefore, after 12 weeks, Samuel and Lewis will have the same number of rocks in their collections.
To find the number of rocks each will have at that point, we can substitute x = 12 into either equation:
Samuel: y = 18 + 4(12) = 66
Lewis: y = 30 + 3(12) = 66
Therefore, both Samuel and Lewis will have 66 rocks in their collections after 12 weeks.
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 Response area.
Let Amy's age be x. Then, according to the problem, Billy's age is (x - 6), since he is 6 years younger than Amy. We also know that the sum of their ages is 22:
x + (x - 6) = 22
Simplifying the equation, we get:
2x - 6 = 22
Adding 6 to both sides, we get:
2x = 28
Dividing by 2, we get:
x = 14
Therefore, Amy is currently 14 years old and Billy is 8 years old.
In 8 years, Amy will be (14 + 8) = 22 years old, and Billy will be (8 + 8) = 16 years old.
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)
To solve the system of equations:
3x + 2y = 2
-2x + y = 8
We can use the elimination method. Multiply the second equation by 2:
-4x + 2y = 16
Add it to the first equation:
3x - 4x + 2y + 2y = 2 + 16
Simplify and solve for y:
-2y = 18
y = -9
Substitute this value of y into the second equation and solve for x:
-2x - 9 = 8
-2x = 17
x = -8.5
Therefore, the solution to the system of equations is (-8.5, -9).
you were wrong
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)
I apologize for my mistake. Upon checking again, I realized that my previous response was incorrect.
To solve the system of equations:
3x + 2y = 2
-2x + y = 8
We can use the substitution method. Solve the second equation for y:
y = 8 + 2x
Substitute this into the first equation and solve for x:
3x + 2(8 + 2x) = 2
Simplify and solve for x:
7x + 16 = 2
7x = -14
x = -2
Substitute this value of x into the second equation and solve for y:
-2(-2) + y = 8
y = 12
Therefore, the solution to the system of equations is (-2, 12).
you were wrong again, use the mutiple choices
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)
The correct solution to the system of equations is (-2, 12).
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=Response area
Let p be the number of pens and m be the number of markers bought.
We know the total number of pens and markers bought is 19:
p + m = 19
We also know the total cost of the pens and markers is $11.50:
0.25p + 0.75m = 11.50
Therefore, the system of equations that could be used to solve for p and m 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=Response area
Let g be the number of pounds of granola and r be the number of pounds of raisins added to make 15 pounds of trail mix.
From the problem, we know that:
g + r = 15 (to make a total of 15 pounds of trail mix)
2g + 4.5r = 37.5 (to keep the total cost at $37.50)
Therefore, the system of equations that could be used to solve for g and r is:
g + r = 15
2g + 4.5r = 37.5
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
Let p be the number of petunias and b be the number of begonias that Michelle bought.
From the problem, we know that:
p + b = 22 (total number of plants)
7p + 8b = 163 (total cost of the plants)
We can use the substitution method to solve for one of the variables. Solve the first equation for p:
p = 22 - b
Substitute this expression for p in the second equation and solve for b:
7(22 - b) + 8b = 163
154 - 7b + 8b = 163
b = 9
Substitute this value of b in the first equation and solve for p:
p + 9 = 22
p = 13
Therefore, Michelle bought 13 petunias.
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:
x + y = 164
An equation for the total cars and trucks for dealership B:
2x + 1/2y = 229
How many cars did dealership A sell?
How many trucks did the dealership B sell?
The equation for the total cars and trucks sold at dealership A is x + y = 164, where x is the number of cars and y is the number of trucks sold at dealership A.
The equation for the total cars and trucks sold at dealership B is 2x + 1/2y = 229, where x is the number of cars and y is the number of trucks sold at dealership B.
From the first equation, we can solve for y in terms of x:
y = 164 - x
Substitute this expression for y in the second equation:
2x + 1/2(164 - x) = 229
Simplify and solve for x:
2x + 82 - 1/2x = 229
3/2x = 147
x = 98
Substitute this value of x in the first equation to find the number of trucks sold at dealership A:
y = 164 - x = 164 - 98 = 66
Therefore, dealership A sold 98 cars and 66 trucks, and dealership B sold 196 cars and (229 - 196)/0.5 = 66 trucks.