Chapter 6.3, Problem 24PPS

To determine

To solve the system of equations using elimination method

Answer to Problem 24PPS

  $x=2$

  $y=1$

Explanation of Solution

Given:

Equations:

  $\begin{array}{l}4(x+2y)=8\\ 4x+4y=12\end{array}$

Calculation:

Let the equations be numbered as

  $4(x+2y)=8\to \text{(1)}$

  $4x+4y=12\to \text{(2)}$

Expand equation (1) as follows:

  $4x+8y=8\to \text{(3)}$

Subtract (3) from (2), so that x is eliminated.

  $\begin{array}{l}4x+4y=12\\ \frac{-4x-8y=-8}{-4y=-4}\text{ [When subtracting the sign of (3) changes]}\end{array}$

  $\begin{array}{c}-4y=-4\text{ [Divide }-4\text{ on both sides]}\\ y=\frac{-4}{-4}\\ y=1\end{array}$

Substitute the value of $y=1$ in one of the equations.

Say, equation (2)

  $\begin{array}{l}4x+4(1)=12\\ 4x+4=12\text{ [Subtract 4 on both sides]}\\ 4x=12-4\\ 4x=8\\ x=\frac{8}{4}\text{ [Divide 4 on both sides]}\\ x=2\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=2$ and $y=1.$