Jason L. answered • 09/01/16
Tutor
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Graduate Student Who Loves to Do Math
-2x + 3y = 7.5
7x - 2y = -2.5
Set each into slope intercept form.
3y = 7.5 + 2x
y= 2.5 + 2x/3
-2y = -2.5 -7x
y= 7x/2 + 5/4
Since the 2 lines have different slopes, then it is guaranteed they intersect and thus it is a linear system. If the 2 lines had the same slope, then they would never intersect (they'd either be the same line if the intercepts are also the same or they'd be parallel) and would then not be a linear system.
David S.
tutor
Looks like the 2.5 part doesn't change the slope. The slope for the first equation is the coefficient in the x-term: 2/3; for the second equation it is 7/2. What did change was the y-intercept: instead of 5/4 it would be -5/4.
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09/01/16
Matthew H.
09/01/16