Determine the number of solutions to this system of linear equations

Question

2x + y = 6
4 x + 2 y = 8

Answer 1

To determine the number of solutions to this system of linear equations, we can rewrite them in slope-intercept form, which is y = mx + b.

For the first equation, 2x + y = 6, we can subtract 2x from both sides to isolate y:
y = -2x + 6

For the second equation, 4x + 2y = 8, we can divide the entire equation by 2 to simplify it:
2x + y = 4

Now that we have both equations in slope-intercept form, we can compare their slopes (m-values).

For the first equation, the slope is -2.
For the second equation, the slope is -2.

Since the slopes of both equations are equal, we can conclude that the lines are parallel.

When two lines are parallel, they never intersect, which means there are no common solutions to the system of equations.

Therefore, the number of solutions to this system of linear equations is zero.