SOLUTION: Consider the following system of equations: {4x-7y=-5 5x+3y=29 Does the system have: one solution, no solution or infinite solutions?d

Question 201818: Consider the following system of equations:
{4x-7y=-5
5x+3y=29
Does the system have: one solution, no solution or infinite solutions?d
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Remember (1) if slopes are different, lines intersect,
and this is one solution
(2) If lines are parallel, and lie on top of each other,
They are coincident, and have infinite solutions.
(3) if lines are parallel, but not coincident, they have no solutions.
.
Since slope is best indicator of parallelism, the slope intercept is valuable. Usually best to transform to this style.
.
For this problem
.
(1) 4x-7y = -5,,,,y= (4/7)x + (5/7)
.
(2) 5x +3y =29,,,,y = (-5/3)x + (29/3)
.
As these have different slopes, they are not parallel, and have one solution.
.
Ref ( 4,3) is solution
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