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A student submitted the following answer to the graphing systems problem:

Is that student correct? Why or why not? If not, what would the solution be?

A student submitted the following answer to the graphing systems problem Is that student correct Why or why not If not what would the solution be class=

Respuesta :

Answer: No, she is not correct.

Step-by-step explanation:

Since we have given that

[tex]6x+y=36-----------(1)\\\\5x-y=8---------------(2)[/tex]

First we check the consistency of system of equations:

[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]

here , [tex]a_1=6,b_1=1,c_1=36\\a_2=5,b_2=-1,c_2=8[/tex]

so, it becomes,

[tex]\frac{6}{5}\neq \frac{1}{-1}\neq \frac{36}{8}[/tex]

So, it is consistent and it is an intersecting lines.

So, it would have a unique solution.

From Eq(1), we have,

[tex]6x+y=36\\\\y=36-6x[/tex]

Put it in eq(2), we have

[tex]5x-y=8\\\\5x-(36-6x)=8\\\\5x-36+6x=8\\\\11x-36=8\\\\11x=36+8\\\\11x=44\\\\x=\frac{44}{11}=4[/tex]

So, x=4 and

[tex]y=36-6x=36-6\times 4=36-24=12[/tex]

so, the solution point of this line will be (4,12).

No, she is not correct.

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