Chapter 6, Problem 39SGR

To determine

Tocalculate : To solve the two equations using elimination method.

Answer to Problem 39SGR

The value of x is 6and the value of y is-1.

Explanation of Solution

Given information :

Given the two equations:

  $\begin{array}{l}2x+9y=3\\ 5x+4y=26\end{array}$

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:

  $2x+9y=3$ .........Equation 1

  $5x+4y=26$ .........Equation 2

Multiplying Equation1 by number 5, we get:

  $(2x+9y=3)\times 5$

  $\Rightarrow 10x+45y=15$ …..Equation 3

Multiplying Equation 2 by number 3, we get:

  $(5x+4y=26)\times 2$

  $\Rightarrow 10x+8y=52$ ......... Equation 4

Subtracting Equation 4from Equation 3, we get:

  $\begin{array}{l}(10x+45y)-(10x+8y)=15-52\\ \Rightarrow 10x+45y-10x-8y=-37\\ \Rightarrow 37y=-37\\ \Rightarrow y=\frac{-37}{37}\\ \Rightarrow y=-1\end{array}$

Putting the value of yinto Equation 1, we get:

  $\begin{array}{l}2x+9(-1)=3\\ \Rightarrow 2x-9=3\\ \Rightarrow 2x=12\\ \Rightarrow x=\frac{12}{2}\\ \Rightarrow x=6\end{array}$

So the value of x is 6and the value of y is equal to -1.