if a pair of linear equations give parallel line on plotting the graph. What type of solution is given by such equations.
Answers
Step-by-step explanation:
We know that a linear equation in two variables represent a straight line. If we have the pair of equations that means we have two straight lines. Now the following possibilities are there:
1. Lines may intersect
2. Lines may be coincident
3. Lines may be parallel
i) When lines intersect in a single point we have one solution. Such solution is called a unique solution. (Consistent pair of equations).
ii) When lines are coincident every point on the lines is a solution so we have many solutions. [Dependent (consistent) pair of equations].
iii) When lines are parallel there is no common point satisfying both the equations. So we have no solution. (Inconsistent pair of equations).
The lines represented by the equation a1x+b1y+c1=0 and a2x+b2y+c2=0 are
i) intersecting, then a1a2≠b1b2.
ii) coincident, then a1a2=b1b2=c1c2.
iii) parallel, then a1a2=b1b2≠c1c2.
In fact, the converse is also true for any pair of lines.
Answer:
Parallel lines (I wrote parallel line didn't put an s)
hope it helps you
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