Question

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?

Answer 1

Answer: No, she is not correct.

Step-by-step explanation:

Since we have given that

$6x+y=36-----------(1)\\\\5x-y=8---------------(2)$

First we check the consistency of system of equations:

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

here , $a_1=6,b_1=1,c_1=36\\a_2=5,b_2=-1,c_2=8$

so, it becomes,

$\frac{6}{5}\neq \frac{1}{-1}\neq \frac{36}{8}$

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

So, it would have a unique solution.

From Eq(1), we have,

$6x+y=36\\\\y=36-6x$

Put it in eq(2), we have

$5x-y=8\\\\5x-(36-6x)=8\\\\5x-36+6x=8\\\\11x-36=8\\\\11x=36+8\\\\11x=44\\\\x=\frac{44}{11}=4$

So, x=4 and

$y=36-6x=36-6\times 4=36-24=12$

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

No, she is not correct.