Question

The equation Ax+By=10 goes through the coordinates (6,5) and (-2,-5)

Answer 1

ANSWER

Given:

$Ax+By=10$

If this line goes through
$(6,5)$
then, the point must satisfy it.

$6A+5B=10 - - (1)$


Similarly,

$(-2,-5)$
must also satisfy this equation.

$- 2A - 5B=10 - - (2)$

Now we add equation (1) and (2)

$\Rightarrow 4A = 20$

Dividing through by 4 gives,

$A = 5$

We substitute in to equation 1 to find B

$6(5)+5B=10$

$5B=10 - 30$

$5B= - 20$

$B= - 4$