Chapter 6, Problem 50SGR

To determine

Tocalculate: To solve the two equations using elimination method.

Answer to Problem 50SGR

The value of x is 3 and the value of y is equal to 5.

Explanation of Solution

Given information:

Given the two equations:

  $\begin{array}{l}11x-6y=3\\ 5x-8y=-25\end{array}$

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:

  $11x-6y=3$ ……Equation 1

  $5x-8y=-25$ ……Equation 2

Multiplying the Equation 1 by 5:

  $(11x-6y=3)\times 5$

  $\Rightarrow 55x-30y=15$ ….Equation 3.

Multiplying the Equation 2 by 11:

  $(5x-8y=-25)\times 11$

  $\Rightarrow 55x-88y=-275$ ….Equation 4

Now subtracting Equation 4 from Equation 3, we get:

  $\begin{array}{l}\Rightarrow (55x-30y)-(55x-88y)=15-(-275)\\ \Rightarrow 55x-30y-55x+88y=15+275\\ \Rightarrow 58y=290\\ \Rightarrow y=\frac{290}{58}\\ \Rightarrow y=5\\ \end{array}$

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

  $\begin{array}{l}11x-6(5)=3\\ \Rightarrow 11x-30=3\\ \Rightarrow 11x=3+30\\ \Rightarrow 11x=33\\ \Rightarrow x=\frac{33}{11}\\ \Rightarrow x=3\end{array}$

So the value of x is 3 and the value of y is equal to 5.