Question

3. Lin is solving this system of equations:S 6x – 5y = 343x + 2y = 83. She starts by rearranging the second equation to isolate the y variable: y = 4 -1.5%. She then substituted the expression 4 - 1.5x for y in the first equation, asshown below:--6x – 5(4 – 1.5x) = 346x – 20 – 7.5x = 34-1.5x = 54x = -36y = 4 – 1.5xy = 4 - 1.5 • (-36)y = 58.

Answer 1

We are given the following system of equations:

`\begin{gathered} 6x-5y=34,(1) \\ 3x+2y=8,(2) \end{gathered}`

We are asked to verify if the point (-36, 58) is a solution to the system. To do that we will substitute the values x = -36 and y = 58 in both equations and both must be true.

Substituting in equation (1):

`6(-36)-5(58)=34`

Solving the left side we get:

`-506=34`

Since we don't get the same result on both sides this means that the point is not a solution.

Now, we will determine where was the mistake.

The first step is to solve for "y" in equation (2). To do that, we will subtract "3x" from both sides:

`2y=8-3x`

Now, we divide both sides by 2:

`y=(8)/(2)-(3)/(2)x`

Solving the operations:

`y=4-1.5x`

Now, we substitute this value in equation (1), we get:

`6x-5(4-1.5x)=34`

Now, we apply the distributive law on the parenthesis:

`6x-20+7.5x=34`

This is where the mistake is, since when applying the distributive law the product -5(-1.5x) is 7.5x and not -7.5x.