#### If a pair of equations plotted on a graph gives two parallel lines, then the pair of equations has no solution.

If a pair of equations plotted on a graph gives two parallel lines, then the pair of equations has no solution.

#### A person paddles a canoe 30 miles downstream in 2 hours. If the return trip takes 3 hours, then the speed of paddling is ____.

Let 'x' miles/hr be the paddling speed and 'y' miles/hr be the speed of the current. Speed of the man while going downstream = (x + y) miles/hr Speed of the man while going upstream = (x − y) miles/hr We know that, Distance = Speed × Time Downstream: Time taken is 2 hrs and Distance is 30 miles ⇒ x – y = 10 ----- (ii) ⇒ (x + y) + (x − y) = 15 + 10 Adding equations (i) and (ii), we get ⇒ 2x = 25 ⇒ x = 12.5 Hence, the speed of paddling is 12.5 m/hr.

#### The degree of a linear equation in two variables is ____.

The degree of a linear equation in two variables is 1.

#### A linear equation in two variables is also called a simultaneous equation.

A linear equation in two variables is also called a simultaneous equation.

#### A pair of linear equations which have no solutions are called inconsistent pair of linear equations.

A pair of linear equations which have no solutions are called inconsistent pair of linear equations.

#### The solution of the system of equations x = 0 and y = 0 is ____.

The ordered pair which satisfies the given system of equations is (0, 0).

#### The larger of two complementary angles is twice the smaller. Then the angles are ____.

Two angles are said to be complementary, if their sum is equal to 90°. Let the angles be x and y. x + y = 90 ---- (i) suppose x is the larger angle. ⇒ x = 2y As per the problem, x – 2y = 0 ----- (ii) Subtracting equation (ii) from equation (i), we get ⇒ -3y = -90 ⇒ 3y = 90 ⇒ y = 30 Substituting the value of y in equation (i), we get x = 60 Hence, the angles are 60° and 30°.

#### A pair of linear equations which have infinitely many distinct solutions are called a dependent consistent pair of linear equations.

Pair of linear equations which have infinitely many distinct solutions are called a dependent consistent pair of linear equations.

#### If two lines are parallel, then the pair of equations have ____ solutions.

If the lines are parallel, then the pair of equations has no solutions.