Chapter 6, Problem 18PT

To determine

Tocalculate : To solve the two equations using elimination method.

Answer to Problem 18PT

The value of x is 4 and the value of y is equal to -1.

Explanation of Solution

Given information :

Given the two equations:

  $\begin{array}{l}3x+5y=7\\ 2x-3y=11\end{array}$

Formula Used:

For elimination method, we multiply both the number with two different constant number the we add or subtract the equations, eliminate anyone first variable and then get the value of second variable. Further we put the value of the second variable in any of the equations and get the value of the first variable.

Calculation:

Equations:

  $3x+5y=7$ …..Equation 1

  $2x-3y=11$ …..Equation 2

Multiplying the first equation by 2 and second equation by 3:

  $\begin{array}{l}(3x+5y=7)\times 2\\ (2x-3y=11)\times 3\end{array}$

We get-

  $6x+10y=14$ …..Equation 3

  $6x-9y=33$   .........Equation 4

Now subtracting Equation 3 from Equation 4:

  $\begin{array}{l}(3x+5y=7)\times 2\\ (2x-3y=11)\times 3\\ \\ 6x+10y=14\\ (6x-9y)-(6x+10y)=33-14\\ \Rightarrow 6x-9y-6x-10y=19\\ \Rightarrow -19y=19\\ \Rightarrow y=-\frac{19}{19}\\ \Rightarrow y=-1\end{array}$

Putting the value of y into Equation 1, we get:

  $\begin{array}{l}3x+5(-1)=7\\ \Rightarrow 3x-5=7\\ \Rightarrow 3x=12\\ \Rightarrow x=\frac{12}{3}\\ \Rightarrow x=4\\ \\ \end{array}$

So the value of x is 4and the value of y is equal to -1.