Question

if x is the number of years since 2000 and y is the percent of people using travel services the following equations represent the percent of people using travel agents and the percent of people using the internet to plan travel. y=-2x+30 y=6x+41 Find the year travel agents and the Internet were used equally

Answer 1

We need to solve a system of two variables with two equations, using elimination method.

y=-2x+30 (1)

y=6x+41​ (2)

We are going to multiply first equation by 3, doing so the equation (1) can be written as:

3y = -6x + 90 (1)

Then, we are going to add the last equation to the second equation

3y = -6x + 90 (1)

+ y= 6x + 41​ (2)

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4y = 131

y = 131 / 4 Isolating y

y= 131/ 4

Then, we replace y= 131/4 in the first equation and solve for x

`\begin{gathered} (131)/(4)=-2x+30 \\ (131)/(4)-30=-2x\text{ Transposing 30 to the other side of the equation} \\ (131)/(4)-(120)/(4)=-2x\text{ Converting 30 to an improper fraction} \\ (11)/(4)=-2x\text{ Operating homogeneous fractions} \\ ((11)/(4))/(-2)=-(2)/(-2)x\text{ Dividing by -2 on both sides of the equation} \\ -(11)/(8)=x \end{gathered}`

Since -11/8 is equal to -1.4 and x represents the number of years since 2000, then the year travel agents and the Internet were used equally was 1998.