To find what the answer is for this problem, we need to find out whether each of them have infinite, no, or single solutions. We can do this individually.
Starting with the first one, we need to convert both of the equations into slope-intercept form. y = -2x + 5 is already in that form, now we just need to do it to 4x + 2y = 10.
2y = -4x + 10 y = -2x +5
Since both equations give the same line, the first one has infinite solutions.
Now onto the second one. Once again, the first step is to convert both of the equations into slope-intercept form.
x = 26 - 3y becomes 3y = -x + 26 y = -1/3x + 26/3
2x + 6y = 22 becomes 6y = -2x + 22 y = -1/3 x + 22/6
Since the slopes of these two lines are the same, that means that they are parallel, meaning that this one has no solutions.
Now the third one. We do the same steps.
5x + 4y = 6 becomes 4y = -5x + 6 y = -5/4x + 1.5
10x - 2y = 7 becomes 2y = 10x - 7 y = 5x - 3.5
Since these two equations are completely different, that means that this system has one solution.
