what does the solution of (-2,-5) for the system of equations 9x-8y=22 and -10x + 5y= -5 indicate on the coordinate plane?

Mathematics

1 answer:

andre [41]3 years ago

5 0

Answer:

see the explanation

Step-by-step explanation:

we have

$9x-8y=22$ ----> equation A

$-10x+5y=-5$ ---> equation B

we know that

The solution of the system of equations by graphing is the intersection point both graphs

The solution of the system is the point (-2,-5)

therefore

The point (-2,-5) indicate on the coordinate plane the intersection point both lines ( a common point for both lines)

see the attached figure to better understand the problem

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Work Shown:

6x-y = -3 is the same as 6x-y+3 = 0

6x-y+3 = 0 is the form Ax+By+C = 0 with A = 6, B = -1, C = 3.

The distance d that line is from the point (p,q) = (6, 2) is found by the following

$d = \frac{A*p+B*q+C}{\sqrt{A^2+B^2}}\\\\d = \frac{6*6-1*2+3}{\sqrt{6^2+(-1)^2}}\\\\d = \frac{36-2+3}{\sqrt{36+1}}\\\\d = \frac{37}{\sqrt{37}}\\\\d = \frac{37\sqrt{37}}{37}\\\\d = \sqrt{37}\\\\d \approx 6.08276\\\\$