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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.

3 Lin Is Solving This System Of EquationsS 6x 5y 343x 2y 83 She Starts By Rearranging The Second Equation To Isolate The Y Variable Y 4 15 She Then Substituted class=
3 Lin Is Solving This System Of EquationsS 6x 5y 343x 2y 83 She Starts By Rearranging The Second Equation To Isolate The Y Variable Y 4 15 She Then Substituted class=

Sagot :

We are given the following system of equations:

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

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):

[tex]6(-36)-5(58)=34[/tex]

Solving the left side we get:

[tex]-506=34[/tex]

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:

[tex]2y=8-3x[/tex]

Now, we divide both sides by 2:

[tex]y=\frac{8}{2}-\frac{3}{2}x[/tex]

Solving the operations:

[tex]y=4-1.5x[/tex]

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

[tex]6x-5(4-1.5x)=34[/tex]

Now, we apply the distributive law on the parenthesis:

[tex]6x-20+7.5x=34[/tex]

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

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