what is the number of solutions to this system of linear equations:
2x + y = 6 and 4x + 2y = 8
A. 1
B. 0
C. 2
D. infinite
AAAaannndd the bot gets it wrong yet again!
Sorry, but twice the first equation is
4x+2y = 12
so in fact, the lines are parallel, and there are no solutions.
I apologize for the mistake. You are correct that the second equation should be 4x + 2y = 12, and the two equations represent parallel lines. Therefore, there are no solutions to this system of linear equations. The correct answer is B.
To determine the number of solutions to the system of linear equations, we can use the concept of slopes and intercepts.
First, let's write the given system of equations in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Equation 1: 2x + y = 6
Rearranging the equation, we get:
y = -2x + 6
Equation 2: 4x + 2y = 8
Dividing the entire equation by 2, we have:
2x + y = 4
Rearranging the equation, we get:
y = -2x + 4
Now we can compare the slopes of the two equations. Both equations have a slope of -2, which means they are parallel lines.
Parallel lines do not intersect, so they have no common solution. Thus, the system of equations has no solution.
Therefore, the answer is:
B. 0 (no solution)