complete the following table with the appropriate answer for the given pairs of the linear equations
Answers
Answer:
2/4 = 1/2
-3/-6 = 1/2
-8/-9 = 8/9
Inconsistent
No solutions
Parallel lines
1/3
-2/4 = -1/2
0/-20 = 0
Consistent
One solution
Intersecting lines
1/2
1/2
-6/-12 = 1/2
Consistent
Many solutions
Coincident lines
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Given: Pair of linear equations
To Find: Number of solution, consistency and graphical representation of given pair of linear equations.
Concept: Graphical representation & algebraic interpretation of pair of linear equations.
When pair of lines represented by equation a1x+b1y+c=0 ; a2x+b2y+c2=0; then
S.r Comparing of ratios Graphical representation Alg representation
1 A1/a2 ≠ b1/b2 Intersecting line Exactly one solution
2 A1/a2=b1/b2=c1/c2 Coincident line Infinitely many soln
3 A1/a2=b1/b2≠ c1/c2 Parallel lines No solution.
Equations of lines are consistent when they have either one solution or many solution. If they had no solution then they are inconsistent.
Step-by-step explanation:
Now using the above concept, the solution is tabled below-
Pair of eqns A1/a2; b1/b2;c1/c2 Consistent/inconsistent One/many/nosol
Intersecting/coincident/parallel lines
2x-3y-8=0;
4x-6y-9=0 ½; 1/2; 8/9 in consistent No solution Parallel lines
x-2y=0;
3x+4y-20=0 1/3; -1/2; 0/20 consistent One solution Intersecting line
X+y=6
2x+2y=12 ½; ½; ½ consistent Many solutions Coincident line
Project Code: #SPJ2