Question

Solve the following system of linear equations by addition. Indicate whether thegiven system of linear equations has one solution, has no solution, or has an infinitenumber of solutions. If the system has one solution, find the solution.s 4x + y = - 23| 7x + 7y = 7Answer 2 PointsKeypadKeyboard ShortcutsSelecting an option will enable input for any required text boxes. If the selected optiondoes not have any associated text boxes, then no further input is required.O One SolutionO No SolutionO Infinite Number of Solutions

Answer 1

Given:

$\begin{gathered} 4x+y=-27 \\ 7x+7y=7 \end{gathered}$

Find : Solution and number of solution.

Sol:.

$\begin{gathered} 4x+y=-27\ldots\ldots\ldots\ldots\text{.}(1) \\ 7x+7y=7\ldots\ldots\ldots\ldots\ldots\text{.}(2) \end{gathered}$

Subtract the equation (2) to 7 times of equation (1)

$\begin{gathered} 7(4x+y)=-27\times7 \\ 28x+7y=-189 \end{gathered}$$\begin{gathered} eq(2)-eq(1) \\ 7x+7y-(28x-7y)=7-(-189) \\ -21x=196 \\ x=\frac{196}{-21} \\ x=-9.33 \end{gathered}$$\begin{gathered} 7x+7y=7 \\ 7(-9.33)+7y=7 \\ -65.33+7y=7 \\ 7y=72.33 \\ y=\frac{72.33}{7} \\ y=10.33 \end{gathered}$

So here only one solution i.e. (-9.33,10.33)