Chapter 0, Problem 53PG

To determine

To solve the system of equation

Answer to Problem 53PG

  $x=3$ and $y=-1$ is solution of system.

Explanation of Solution

Given information:

  $\begin{array}{l}4x-5y=17\\ 3x+4y=5\end{array}$

Calculation:

Let the equations be (1), (2) respectively.

Taking (1)

  $4x-5y=17$

Rearranging,

  $x=\frac{17+5y}{4}$ (3)

Put value of x in (2),

  $3(\frac{17+5y}{4})+4y=5$

Solving,

  $\frac{51+15y}{4}+4y=5$

Taking LCM,

  $\frac{51+15y+16y}{4}=5$

and,

  $51+15y+16y=20$

Adding terms,

  $31y=20-51$

So,

  $y=-1$

Put value of y in (3)

x = $\frac{17+5(-1)}{4}$

Solving,

  $x=\frac{17-5}{4}$

So,

  $x=\frac{12}{4}$

Hence, $x=3$ and $y=-1$ is solution of system.