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