Question

Solve the following system of linear equations by addition. Indicate whether the given system of linearequations has one solution, has no solution, or has an infinite number of solutions. If the system has onesolution, find the solution.5 - 3x + y = 19ly=x+3AnswerKeypadKeyboard ShortcutsSelecting an option will enable input for any required text boxes. If the selected option does not have anyassociated text boxes, then no further input is required.O One SolutionO No SolutionInfinite Number of Solutions

Answer 1

Given the system of equation

`\begin{cases}-3x+y=19 \\ y=x+3\end{cases}`

Rewrite the equation above as

`\begin{cases}-3x+y=19 \\ x-y=-3\end{cases}`

Using addition method, add the two equations to eliminate y

`\begin{gathered} (-3x+x)+(y-y)=(19-3) \\ -2x=16 \\ (-2x)/(-2)=(16)/(-2) \\ x=-8 \end{gathered}`

Substitute x=-8 in the second equation to find y

`\begin{gathered} y=x+3 \\ y=-8+3 \\ y=-5 \end{gathered}`

Hence, the system of equation has one solution, the solution is ( -8 , -5 )

One Solution ( -8 , -5 )