Chapter 6, Problem 14PT

To determine

To solve: the system of equations using elimination method.

Answer to Problem 14PT

The solution is: $x=14,y=10$

Explanation of Solution

Given:

J received 24 issues this year.

The number of fashion issues is 6 less than twice the number of sports issues.

Calculation:

Assume the number fashion issues is: $x$ .

Again, the number of sports issues is: $y$ .

Here the equations are:

  $x+y=24\dots \dots (1)$

And,

  $x=2y-6\dots \dots$ (2)

The strategy is to solve the system of equations using elimination method.

Substitute the value of $x$ in (1) to get:

  $2y-6+y=24$

  $3y-6+6=24+6$

  $\frac{3y}{3}=\frac{30}{3}[$ Divide both sides by 3]

  $y=10$

Again, from equation (2),

  $x=2(10)-6$

  $x=20-6$

  $x=14$

Hence, the solution is: $x=14,y=10$

Conclusion:

Hence, the solution is: $x=14,y=10$