Asked by Y/N

Estimate the solution to the system of these linear equations based on the graph. y=2x+3 y=12x+6 (1 point) Responses (2, 7) left parenthesis 2 comma 7 right parenthesis (−2, 7) left parenthesis negative 2 comma 7 right parenthesis (2,−7) left parenthesis 2 comma negative 7 right parenthesis (7, 2) left parenthesis 7 comma 2 right parenthesis
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Estimate the solution to the system of these linear equations based on the graph. y=−x+6 y=3x−2 (1 point) ()
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Determine the number of solutions to this system of linear equations: 2x+y=6 4x+2y=8 (1 point) Responses 2 2 infinite infinite 1 1 0 0
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Solve the system of equations. 4x−8y=−36 −6x+y=32 (1 point) (, )
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Solve the system of equations. 6x−3y=−6 9x−3y=−18 (1 point) (, )
Answered by GPT 3.5
(2, 7)
Answered by GPT 3.5
The solution to the system of equations y = -x + 6 and y = 3x - 2 is approximately (2, 4) based on the graph.
Answered by GPT 3.5
There are infinite solutions to this system of linear equations because both equations are equivalent (each equation is a multiple of the other).
Answered by GPT 3.5
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method in this case.

We have:
4x - 8y = -36 (1)
-6x + y = 32 (2)

We can multiply equation (2) by 8 to match the coefficient of y in equation (1):
-48x + 8y = 256 (3)

Now, we add equations (1) and (3):
4x - 8y + (-48x + 8y) = -36 + 256
-44x = 220
x = -5

Now, we can substitute the value of x back into one of the original equations. Let's use equation (1):
4(-5) - 8y = -36
-20 - 8y = -36
-8y = -16
y = 2

Therefore, the solution to the system of equations 4x - 8y = -36 and -6x + y = 32 is (-5, 2).
Answered by GPT 3.5
To solve this system of equations, we can see that both equations have the same the equation -3y but different constants on the right side. This implies that the lines representing these two equations are parallel, and therefore they do not intersect.

The system of equations:
6x - 3y = -6
9x - 3y = -18

The second equation is just the first equation multiplied by 3. Since both equations are equivalent after multiplication, they represent the same line. Thus, the system does not have a unique solution. Therefore, the system is inconsistent and has no solution.