Chapter 6.3, Problem 43PFA

To determine

To find the values of x and y for the given equations

Answer to Problem 43PFA

  $x=6$ and $y=-14$

Explanation of Solution

Given:

Equations:

  $\begin{array}{l}3x+y=4\\ 4x+y=10\end{array}$

Calculation:

Let,

  $\begin{array}{l}3x+y=4\to \text{(1)}\\ 4x+y=10\to \text{(2)}\end{array}$

Subtract the equation (2) from equation (1),

  $\begin{array}{l}\Rightarrow (4x+y)-(3x+y)=10-4\\ \Rightarrow 4x+y-3x-y=6\\ \Rightarrow x=6\end{array}$

Substitute the value of x in equation (1)

  $\begin{array}{l}\Rightarrow 3(6)+y=4\\ \Rightarrow 18+y=4\\ \Rightarrow y=4-18\\ \Rightarrow y=-14\end{array}$

Conclusion:

Therefore, the value of $x=6$ and the value of $y=-14$ .