Question

Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or aninfinite number of solutions. If the system has one solution, find the solution.-3x + y = 192y = 6x + 38

Answer 1

`\begin{gathered} -3x+y=19 \\ 2y=6x+38 \end{gathered}`

Here are the steps for substitution method.

1. Equate the second equation to y = .

`\begin{gathered} 2y=6x+38 \\ \text{Divide both sides by -2.} \\ (2y)/(2)=(6x)/(2)+(38)/(2) \\ y=3x+19 \end{gathered}`

2. Plug the value of "y" into the first equation.

`\begin{gathered} -3x+y=19 \\ -3x+(3x+19)=19 \\ -3x+3x+19=19 \\ \text{Subtract 19 on both sides.} \\ -3x+3x+19-19=19-19 \\ 0=0 \end{gathered}`

Since both sides are equal to zero, this means, both equations are just equal to each other. This means the system has infinite number of solutions.