Examine whether the solution set of the system of equations 3x - 4y = -7; 3x - 4y = -9. is consistent or inconsistent.with step by step. dont send through photo. i will mark as brainliest answer
Answers
Answer:
3x -4y=-7 --------(eq1)
3x-4y= -9 --------(eq2)
3/3 =4/4 is not equal to -7/-9
a1/a2=b1/b2 not equal to c1/c2
it means it is a parallel line and parallel line is always inconsistent.
So given eq. is inconsistent
Answer :
Inconsistent
Note:
★ A linear equation is two variables represent a straight line .
★ The word consistent is used for the system of equations which consists any solution .
★ The word inconsistent is used for the system of equations which doesn't consists any solution .
★ Solution of a system of equations : It refers to the possibile values of the variable which satisfy all the equations in the given system .
★ A pair of linear equations are said to be consistent if their graph ( Straight line ) either intersect or coincide each other .
★ A pair of linear equations are said to be inconsistent if their graph ( Straight line ) are parallel .
★ If we consider equations of two straight line
ax + by + c = 0 and a'x + b'y + c' = 0 , then ;
• The lines are intersecting if a/a' ≠ b/b' .
→ In this case , unique solution is found .
• The lines are coincident if
a/a' = b/b' = c/c' .
→ In this case , infinitely many solutions are found .
• The lines are parallel if a/a' = b/b' ≠ c/c' .
→ In this case , no solution is found .
Solution :
Here ,
The given linear equations are ;
3x - 4y = -7
3x - 4y = -9
The given equations can be rewritten as ;
3x - 4y + 7 = 0
3x - 4y + 9 = 0
Clearly ,
a = 3
a' = 3
b = -4
b' = -4
c = 7
c' = 9
Now ,
a/a' = 3/3 = 1
b/b' = -4/-4 = 1
c/c' = 7/9
Clearly ,
a/a' = b/b' ≠ c/c'
Hence ,
The given system is inconsistent as they are parallel .