Write the condition for patients of coefficient of linear equation representing parallel
Answers
Answer:
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The general form for a pair of linear equations in two variables x and y is
a1x + b1y + c1 = 0 and
a1x + b1y + c1 = 0 anda2x + b2y + c2 = 0,
a1x + b1y + c1 = 0 anda2x + b2y + c2 = 0,Where a1, b1, c1, a2, b2, c2 are all real numbers and a12 + b12 ≠ 0, a22 + b22 ≠ 0.
Geometrical representation of pair of linear equations in two variables
The geometrical representation of a linear equation in two variables is a straight line.
Pair of linear equations in two variables:
If we have two linear equations in two variables in a plane, and we draw lines representing the equations, then:
Condition
Result
Lines intersecting at a single point
=>
The pair of equations has a unique solution. The pair of linear equations is consistent
Lines parallel to each other
=>
No solutions. The pair of linear equations is inconsistent.
Coincident lines
=>
Infinite number of solutions. The pair of linear equations is consistent and dependent.
Algebraic interpretation of pair of linear equations in two variables
The pair of linear equations represented by these lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
If then the pair of linear equations has exactly one solution.
If then the pair of linear equations has infinitely many solutions.
If then the pair of linear equations
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Answer:
In other words, the slopes of parallel lines are equal. Note that two lines are parallel if their slopes are equal and they have different y-intercepts. In other words, perpendicular slopes are negative reciprocals of each other. Here is a quick review of the slope/intercept form of a line.We can graphically represent a pair of linear equations as two lines. And lines may intersect, or may be parallel, or may coincide. ... Such a pair is called a dependent pair of linear equations in two variables. Note that a dependent pair of linear equations is always consistent.