Chapter 11.1, Problem 24AYU

To determine

To find: The solution of the given system of equations.

Answer to Problem 24AYU

Solution:

  $x=-\frac{5}{3},y=1$

Explanation of Solution

Given:

  $2x+4y=\frac{2}{3}$

  $3x-5y=-10$

Calculation:

The system of equations is,

  $2x+4y=\frac{2}{3}$

  $3x-5y=-10$

Multiplying the first equation by 5 and the second equation by 4 and then adding these two we get,

  $5(2x+4y)+4(3x-5y)=5\left(\frac{2}{3}\right)+4(-10)$

  $10x+20y+12x-20y=\frac{10}{3}-40$

  $22x=-\frac{110}{2}$

  $x=-\frac{110}{3(22)}$

  $x=-\frac{5}{3}$

Substituting $x=-\frac{5}{3}$ in the first equation we get

  $2\left(-\frac{5}{3}\right)+4y=\frac{2}{3}$

  $-\frac{10}{3}+4y=\frac{2}{3}$

  $4y=\frac{2}{3}+\frac{10}{2}$

  $4y=\frac{12}{2}$

  $4y=4$

  $y=\frac{4}{4}$

  $y=1$

Thus $x=-\frac{5}{3},y=1$ is the solution of the given system of equations.

The graph is as follows: