Determine the number of solutions to the system of linear equations 2x + y = 6 and 4x + 2y = 8. Out of the answers which is correct? 1, 0, infinite or 2?
To determine the number of solutions to the system of linear equations, we can use the concept of the slope-intercept form, which is y = mx + b.
First, we can rewrite the given equations in slope-intercept form:
2x + y = 6
y = -2x + 6
4x + 2y = 8
2y = -4x + 8
y = -2x + 4
Comparing the two equations, we notice that they have the same slope, which is -2. This means that the two lines are parallel.
When two lines are parallel, they never intersect. Therefore, there are no solutions to the system of linear equations.
The correct answer is 0.