Pair of Linear Equations in Two Variables

If a pair of linear equations is consistent, then the lines are:

• Parallel

• Coincident

• Intersecting

• Intersecting or coincident

The pair of equations y = 0 and y = -7 has

• One solution

• Two solutions

• Infinitely many solutions

• No solution

ASSERTION :The lines 2x-5y=7 and 6x-15y=8 are parallel lines.

REASON : The system of linear equations a₁x + b₂y + c₁=0 and a₂x + b₂y + c₂=0 have infinitely many solutions if a₁/a₂ = b₁/b₂ = c₁/c₂

• Both Assertion and Reason are true and Reason is the correct explanation of assertion.

• Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

• Assertion is true but Reason is false

• Assertion is false but Reason is true

The graph of x = -2 is a line parallel to the

• y-axis

• x-axis

• both x- and y-axis

• none of these

If in the equation x+2y=10, the value of y is 6, then the value of x will be

• -2

• 2

• -4

• 5

ASSERTION :3x+4y+5=0 and 6x+ky+9=0 represent parallel lines if k=8.

REASON : a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0 represent parallel lines if a₁/a₂₌b₁/b₂≠c₁/c₂

• Both assertion and reason are true and reason is the correct explanation of assertion

• Both assertion and reason are true but reason is not the correct explanation of assertion

• Assertion is true but Reason is false

• Assertion is false but Reason is true

A pair of linear equations a₁x + b₁y + c₁ = 0; a₂x + b₂y + c₂ = 0 is said to be inconsistent, if:

• a₁/a₂≠b₁/b₂

• a₁/a₂=b₁/b₂≠c₁/c₂

• a₁/a₂=b₁/b₂=c₁/c₂

• a₁/a₂≠c₁/c₂

ASSERTION :If the pair of lines are coincident, then we say that pair of lines is consistent and it has a unique solutions.

REASON :If the pair of lines are parallel, then the pair has no solutions and is called inconsistent pair of equation

• Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

• Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

• Assertion is true but Reason is false

• Assertion is false but Reason is true

The pairs of equations x+2y-5=0 and -4x-8y+20=0 have:

• Unique solution

• No solution

• Infinitely many

• None of these

ASSERTION :The linear equation x-2y-3=0 and 3x+4y-20=0 have exactly one solutions.

REASON :The linear equation 2x+3y-9=0 and 4x+6y-18=0 have a unique solution.

• Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

• Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

• Assertion is true but Reason is false

• Assertion is false but Reason is true