Chapter 0, Problem 49PG

To determine

To solve the system of equations

Answer to Problem 49PG

  $x=1,y=1$ are the solution of the system.

Explanation of Solution

Given information:

  $\begin{array}{l}2x+4y=6\\ 7x=4+3y\end{array}$

Calculation:

Let the equations be (1) and (2)

Taking (2),

  $7x=4+3y$

Rearranging,

  $x=\frac{4+3y}{7}$ (3)

Put x in (1)

  $2(\frac{4+3y}{7})+4y=6$

Solving,

  $\frac{8+6y}{7}+4y=6$

Now taking LCM and adding,

  $\frac{8+6y+28y}{7}=6$

Multiplying by 7,

  $8+6y+28y=42$

Now,

  $34y=42-8$

Dividing by 34,

  $y=1$

Put y in (3)

  $x=\frac{4+3(1)}{7}$

Solving,

  $x=\frac{4+3}{7}$

Hence, $x=1,y=1$ are the solution of the system.