Question

The number of girls, g, in a room is four more than two times the number of boys, b. Half of the number of girls in the room minus the number of boys is 2. The equations below represent the situation. Which is true? ; There are infinite solutions to the system. ; There are no solutions to the system. ; There are four girls and zero boys in the room. ; There are eight girls and zero boys in the room.

Answer 1

The given equations to the above question are :

g=4+2b and

\frac{1}{2} g-b=221g−b=2

We need to solve for g and b.

We write the equations in the form ax+by=c.

The first equation is g=4+2b

Subtracting 2b both sides :

g-2b=4.

This is of the form ax+by=c.

The second equation is :

\frac{1}{2} g-b=221g−b=2

Multiplying both sides by 2 to get rid of the denominator 2 the equation reduces to

g-2b=4.This is of the form ax+by=c.

Both the equations are same .This implies the system of equations has infinite number of solutions.

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