The solution to a system of linear equations could be ... (select all that apply)(4 points)
Responses
The Y-Axis
The Y-Axis
The X-Axis
The X-Axis
The Point Where All the Lines Intersect
The Point Where All the Lines Intersect
Infinitely Many Solutions
Infinitely Many Solutions
An Ordereed Pair
An Ordereed Pair
The Graph
The Graph
No Solutions
No Solutions
A Single Number
The Point Where All the Lines Intersect
An Ordered Pair
The Graph
No Solutions
For a system of equations of the form y=mx+b where m is the slope and b is the y-intercept, the system will have
if the slopes are different.
The system will have a single point of intersection if the slopes are different.
Part B
How many solutions does the following system of equations have,
y=23x + 7
y=23x +10
Choose the correct option:
(1 point)
Responses
infinite solutions
infinite solutions
none of the above
none of the above
one soltuion
one soltuion
no solution
The correct option is "no solution".
Match the system of equations in the first column with their corresponding description.
(3 points)
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.
y=8x+4
y=2x+6
y=4x+3
y=4x+2
y=2x+7
y=2x+7
y=8x+4 - Line with slope 8 and y-intercept 4
y=2x+6 - Line with slope 2 and y-intercept 6
y=4x+3 - Line with slope 4 and y-intercept 3
y=4x+2 - Line with slope 4 and y-intercept 2
y=2x+7 - Line with slope 2 and y-intercept 7
Match the system of equations in the first column with their corresponding description.
(3 points)
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.
y=8x+4
y=2x+6
y=4x+3
y=4x+2
y=2x+7
y=2x+7
answer choices:
consistent and dependant
inconsistent
consistent and independant
y=8x+4 - consistent and independent
y=2x+6 - consistent and independent
y=4x+3 - consistent and independent
y=4x+2 - consistent and independent
y=2x+7 - consistent and dependent
Match the system of equations in the first column with their corresponding description.
(3 points)
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.
y=8x+4
y=2x+6
y=4x+3
y=4x+2
y=2x+7
y=2x+7
answer choices:
consistent and dependant
inconsistent
consistent and independant
y=8x+4 - consistent and independent
y=2x+6 - consistent and independent
y=4x+3 - consistent and independent
y=4x+2 - consistent and independent
y=2x+7 - consistent and dependent
WRONG not all of them are the same answer
Apologies for the incorrect response. Here are the correct matches:
y=8x+4 - consistent and independent
y=2x+6 - consistent and independent
y=4x+3 - consistent and independent
y=4x+2 - inconsistent
y=2x+7 - consistent and dependent
For the following system of equations, what is the value of x in the solution?(1 point)
The system of equation is x+3y = 6 and 6x-6y = 4
x=
To find the value of x in the solution, we need to solve the system of equations:
x + 3y = 6,
6x - 6y = 4.
Let's solve the system:
From the first equation, we can isolate x:
x = 6 - 3y.
Now substitute the expression for x in the second equation:
6(6 - 3y) - 6y = 4.
Expand and simplify:
36 - 18y - 6y = 4,
36 - 24y = 4.
Move the constant term to the other side:
-24y = 4 - 36,
-24y = -32.
Divide by -24:
y = (-32) / (-24),
y = 4/3.
Now substitute the value of y back into the expression we found for x:
x = 6 - 3(4/3),
x = 6 - 4,
x = 2.
So, the value of x in the solution is x = 2.
Part A
Rewrite the following system of equations in slope intercept form.
The system of equation is:
−6x+y = 10
−36x+6y=48
(1 point)
Responses
−6x=10−y
−36x=48−6y
negative 6 x is equal to 10 minus y negative 36 x is equal to 48 minus 6 y
y=6x+10
y=6x+8
y is equal to 6 x plus 10 y is equal to 6 x plus 8
y=6x+10
y=36x+48
y is equal to 6 x plus 10 y is equal to 36 x plus 48
None of the above
To rewrite the system of equations in slope-intercept form, we need to solve for y in terms of x.
The given system of equations:
-6x + y = 10
-36x + 6y = 48
For the first equation, rearrange it to isolate y:
y = 6x + 10
For the second equation, divide both sides by 6 to simplify:
-36x + 6y = 48
6y = 36x + 48
y = 6x + 8
Therefore, the system of equations in slope-intercept form is:
y = 6x + 10
y = 6x + 8