Chapter 6, Problem 20SGR

To determine

To calculate : To solve the two equations using substitution method.

Answer to Problem 20SGR

The value of x is 4 and the value of y is equal to 2.

Explanation of Solution

Given information :

Given the two equations:

  $\begin{array}{l}3x+2y=16\\ x=3y-2\end{array}$

Formula Used:

For substitution method, we substitute the value of anyone first variable from first equation to other equation then we find the value of the first variable from that second equation, where there is only one variable unknown. After getting the value of the first variable, we put the value of this variable to any of the two linear equations. And then we find the value of the second variable.

Calculation:

Equations:

  $3x+2y=16$ ......Equation 1

  $x=3y-2$ ...... Equation 2

Putting the value of the y from Equation 2 to Equation 1,we get:

  $\begin{array}{l}3(3y-2)+2y=16\\ \Rightarrow 9y-6+2y=16\\ \Rightarrow 11y=22\\ \Rightarrow y=\frac{22}{11}\\ \Rightarrow y=2\end{array}$

Now putting the value of y into Equation 2, we get:

  $\begin{array}{l}x=3(2)-2\\ \Rightarrow x=6-2\\ \Rightarrow x=4\end{array}$

So the value of x is 4 and the value of y is equal to 2.