The correct statement that describes the solution to this system of equations is:
There is exactly one solution to this system of linear equations and it is (2, 0).
This is because both equations are in the form y = mx + b, where m represents the slope and b represents the y-intercept. In this case, both equations have a slope of 4 and a y-intercept of 2.
Therefore, the lines are not parallel and intersect at a single point, which is (2, 0).
so is there any other answer that i could choose with this?
Check all that apply. Select the statement(s) that correctly describes the solution to this system of equations:
8x−2y=−4
4x−y=−2
(2 points)
Responses
Solve this system by elimination since it is already in standard form and lined up nicely.
There is exactly one solution to this system of linear equations and it is (2, 0).
There are infinite solutions to this system of linear equations.
These lines are parallel, so there is no solution to this system of linear equations.
There is exactly one solution to this system of linear equations and it is (0, -2).
Solve this system by substitution since one of the variables is defined by the other without having to do any math.
The correct statement that describes the solution to this system of equations is:
There is exactly one solution to this system of linear equations and it is (2, 0).
The correct statement that describes the solution to this system of equations is: "There is exactly one solution to this system of linear equations and it is (2, 0)."
The other statements do not accurately describe the solution to this particular system of equations.
To determine the correct statement(s) that describe the solution to this system of equations, we need to solve the system of equations and see what the solution is.
The system of equations is:
8x - 2y = -4
4x - y = -2
We can solve this system of equations using the method of elimination.
First, let's multiply the second equation by 2 to make the coefficients of y the same:
4x - y = -2
2(4x - y) = 2(-2)
8x - 2y = -4
As we can see, the first equation is the same as the second equation. This means that the two lines are actually the same line, and there are infinite solutions to this system of equations.
Therefore, the correct statement that describes the solution to this system of linear equations is: "There are infinite solutions to this system of linear equations."
The other statements are incorrect:
- "There is exactly one solution to this system of linear equations and it is (2, 0)" is incorrect because there are infinite solutions, not just one.
- "These lines are parallel, so there is no solution to this system of linear equations" is incorrect because the lines are not parallel, they are the same line.
- "There is exactly one solution to this system of linear equations and it is (0, -2)" is incorrect because the solution is not (0, -2).
- "Solve this system by substitution since one of the variables is defined by the other without having to do any math" is not applicable in this case since the variables are not defined in terms of each other without any math involved.
Therefore, the correct statement is: "There are infinite solutions to this system of linear equations."