Chapter 6.4, Problem 32HP

To determine

To find the values of a and b .

Answer to Problem 32HP

  $\begin{array}{l}a=3\\ b=22\end{array}$

Explanation of Solution

Given:

System of equations:

  $\begin{array}{l}4x+5y=2\\ 6x-2y=b\end{array}$

Solution: $(3,a)$

Calculation:

Consider the equations $4x+5y=2$

Given that the solution of the system of equations is $(3,a)$ .

Substitute the value of x = 3, in the above equation.

  $\begin{array}{l}\Rightarrow 4x+5y=2\\ \Rightarrow 4(3)+5y=2\\ \Rightarrow 12+5y=2\\ \Rightarrow 5y=-10\\ \Rightarrow y=-2\end{array}$

Substitute the value of x and y in $6x-2y=b$

  $\begin{array}{l}\Rightarrow 6(3)-2(-2)=b\\ \Rightarrow 18+4=b\\ \Rightarrow 22=b\end{array}$

Conclusion:

Therefore, the value of $a=3$ and $b=22.$