Explain how you can determine that the following system has one unique solution – without actually solving the system. 2x+y=4 2y=6-2x

To do so, get every part into slope-intercept form (y = mx + b).

If the slopes are different, there is one solution.

If the slopes the same but the y intercepts different, there is no solution.

If the slopes and y intercepts are the same, there are infinitely many solutions.

2x + y = 4

2y = 6 - 2x

Solve for y on both

y = 4 - 2x

y = 3 - x

They are both different, so there is one solution