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
9 answers
(2, 7)
Estimate the solution to the system of these linear equations based on the graph. y=−x+6 y=3x−2 (1 point) ()
The solution to the system of equations y = -x + 6 and y = 3x - 2 is approximately (2, 4) based on the graph.
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
There are infinite solutions to this system of linear equations because both equations are equivalent (each equation is a multiple of the other).
Solve the system of equations. 4x−8y=−36 −6x+y=32 (1 point) (, )
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).
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).
Solve the system of equations. 6x−3y=−6 9x−3y=−18 (1 point) (, )
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.
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.