Write both equations in the slope intercept form. How many solutions the system will have?
2x + 3y = 12
4x + 6y = 15

Question

Write both equations in the slope intercept form. How many solutions the system will have?
2x + 3y = 12
4x + 6y = 15

whpalmer4 · Answer

Slope intercept form is $$y=mx+b$$where $m$ is slope and $b$ is the y-intercept.

whpalmer4 · Answer

Once you've rewritten the equations, compare their slopes and y-intercepts.  If they have equal slopes, they are parallel or identical.  You determine that by looking at the y-intercepts.  If equal slope and equal y-intercepts, they are the same line, and there are infinitely many solutions.  If equal slope and different y-intercepts, they are parallel, and there are no solutions.  Otherwise, the lines intersect (once) and there is one solution (assuming these lines are in the same plane).