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ANSWER

Given:

[tex]Ax+By=10[/tex]

If this line goes through
[tex](6,5)[/tex]
then, the point must satisfy it.

[tex]6A+5B=10 - - (1)[/tex]


Similarly,

[tex](-2,-5) [/tex]
must also satisfy this equation.

[tex] - 2A - 5B=10 - - (2)[/tex]

Now we add equation (1) and (2)

[tex]\Rightarrow 4A = 20[/tex]

Dividing through by 4 gives,

[tex]A = 5[/tex]

We substitute in to equation 1 to find B

[tex]6(5)+5B=10[/tex]

[tex]5B=10 - 30[/tex]

[tex]5B= - 20[/tex]

[tex]B= - 4[/tex]

The values of A and B of the given equation with the given coordinates are; A = 5 and B = -4

We are told the equation is;

Ax + By = 10

Since the equation goes through (6,5) and (-2,-5), then it means we have two simultaneous equations as;

6A + 5B = 10   ----(eq 1)

-2A - 5B = 10  ----(eq 2)

Add eq 1 to eq 2 to obtain;

4A = 20

A = 20/4

A = 5

Now, put 5 for A in eq 1 to get;

6(5) + 5B = 10

30 + 5B = 10

-5B = 30 - 10

-5B = 20

B = -20/5

B = -4

Thus, in conclusion, the values of A and B are 5 and -4 respectively.

Read more at; https://brainly.com/question/18846487

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